Find the distance between each pair of points. Round to one decimal place. A(-4, 6) and B(3, -7), and E(-6, -5) and F(2, 0).
AB=(
EF=
Answers
To one decimal place, round. points A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).
The distance between AB is [tex]\sqrt{185}[/tex]=13.601 and EF is [tex]\sqrt{89}[/tex]=9.433.
Given that,
To one decimal place, round.
A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).
We have to find the distance between two points that are AB and EF.
1. The distance between 2 points A and B.
A(-4, 6) and B(3, -7).
Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
Here, x₁=-1,x₂=3 and y₁=6,y₂=-7
After substituting we get,
[tex]\sqrt{{(3 -(-1)} )^{2} +(-7 -6 )^{2} }\\[/tex]
[tex]\sqrt{{(3 +1} )^{2} +(-7 -6 )^{2} }\\[/tex]
[tex]\sqrt{{(4} )^{2} +(-13 )^{2} }\\[/tex]
[tex]\sqrt{16 +163}\\[/tex]
[tex]\sqrt{185}[/tex]
13.601
Therefore, the distance between AB is [tex]\sqrt{185}[/tex]=13.601.
2.The distance between 2 points E and F.
E(-6, -5) and F (2, 0).
Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
Here, x₁=-6,x₂=2 and y₁=-5,y₂=0
After substituting we get,
[tex]\sqrt{{(2 -(-6)} )^{2} +(0 -(-5) )^{2} }\\[/tex]
[tex]\sqrt{{(2 +6} )^{2} +(0 +5 )^{2} }\\[/tex]
[tex]\sqrt{{(8} )^{2} +(5 )^{2} }\\[/tex]
[tex]\sqrt{64 +25}\\[/tex]
[tex]\sqrt{89}[/tex]
9.433
Therefore, the distance between EF is [tex]\sqrt{89}[/tex]=9.433.
To learn more about distance visit: https://brainly.com/question/15172156
#SPJ1
Related Questions
The coordinate -2 has a weight of 3, the coordinate 5 has a weight of 1, and the coordinate 6 has a weight of 1. Find the weighted average.
Answers
The weight average of the coordinates is 1
How to determine the weight average?The given parameters are:
Coordinate -2 has a weight of 3Coordinate 5 has a weight of 1Coordinate 6 has a weight of 1The weight average is then calculated as:
Weight average = Sum of (Weight * Coordinate)/Sum of Weights
So, we have:
Weight average = (-2 * 3 + 5 * 1 + 6 * 1)/(3 + 1 + 1)
Evaluate the quotient
Weight average = 1
Hence, the weight average of the coordinates is 1
Read more about average at
brainly.com/question/20118982
#SPJ1
the midpoint of \overline{\text{ab}} ab is m(0, -3)m(0,−3). if the coordinates of aa are (2, 1)(2,1), what are the coordinates of bb?
Answers
If the coordinates of the point a is (2,1) and midpoint is (0.-3), then the coordinates of b is (-2,-7).
Midpoint:
Midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
The formula for midpoint is,
[tex](x_{m},y_{m})= (\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )[/tex]
Where
(x₁,y₁) is the coordinates of the first point and
(x₂,y₂) is the coordinates of the second point
and
[tex](x_m,y_m)[/tex] is the mid point of the first and second points.
Given,
Mid point = (0,-3)
Point a = (2,1)
Here we need to find the point b.
Let (x,y) be the point of b.
Now,
Apply the values on the formula,
Then we get,
[tex](0,-3)=(\frac{2+x}{2},\frac{1+y}{2})[/tex]
Compare the values in order to solve it,
=> 0 = (2 +x)/ 2
=> 0 = 2 + x
=> x = -2
Similarly,
=> -3 = (1 + y)/2
=> -3 x 2 = 1 + y
=> -6 = 1 + y
=> y = -6 - 1
=> y = -7
Therefore, the coordinates of b is (-2,-7).
To know more about Midpoint here.
https://brainly.com/question/28224145
#SPJ4
Stacy has a part time job.
She earns 8 pounds an hour.
She wants to buy a new smartphone costing 220 pounds.
How many hours does she need to work to earn enough to buy it.
Answers
220/8 = 27.5
27.5 x 8 = 220
She’ll have to work 27 hours and 30 minutes to get 220 pounds.
Property to find the sum or product identify the property you used 6 x 43
Answers
The multiplication of 6 × 43 by applying the distributive property of multiplication will be 258.
What is multiplication?The general mathematical operation of multiplying two or more numbers to get a new multiplied number.
If both values are more than or less than one, the resultant multiplication will be greater or smaller than the numbers that will be multiplied.
For reference 4 × 3 = 12 and 4 × 0.5 = 2.
Given the multiplication,
6 × 43
⇒ 6 × (40 + 3)
By applying the distributive property of multiplication,
⇒ 6 × 40 + 6 × 3
⇒ 240 + 18
⇒ 258
Hence "The multiplication of 6 × 43 by applying the distributive property of multiplication will be 258.".
For more information about multiplication,
brainly.com/question/14059007
#SPJ1
3) At midnight, the temperature was 15 degrees
Fahrenheit. When we woke up in the morning, the
temperature was -3 degrees. What was the change in
temperature from midnight to the morning?
Answers
Answer:
Step-by-step explanation:
First of all it has to drop 15 degrees to get to 0.
We have another three degrees to go.
15 - - 3 = 18
The temperature change was 18 degrees from midnight to morning.
23
6. A penny weighs 2.5 grams while a dime weighs about 2.27 grams. How much do a penny and two dimes weigh?
O2.04 g
5.68 g
4.77 g
7.04
Answers
Answer:
7.04
Step-by-step explanation:
2.27
2.27
2.50 equals 7.04
what polynomial is twice the sum of -2x^(2)+5x-3 and 5x^(2)-4 show your work
Answers
The polynomial is twice the sum of -2x² + 5x - 3 and 5x² - 4 is 6x² + 10x - 14.
What polynomial is twice the sum of the given polynomial?Given the polynomials in the question;
-2x² + 5x - 3 and 5x² - 4
First, we find the sum of the polynomials
(-2x² + 5x - 3) + (5x² - 4)
-2x² + 5x - 3 + 5x² - 4
Collect like terms and simplify
-2x² + 5x² + 5x - 3 - 4
3x² + 5x - 7
Next, multiply the polynomial by 2.
2(3x² + 5x - 7)
Using distributive property,
2×3x² + 2×5x +2×-7
6x² + 10x - 14
Therefore, the polynomial is twice the sum of -2x² + 5x - 3 and 5x² - 4 is 6x² + 10x - 14.
Learn more about polynomials here: https://brainly.com/question/20121808
#SPJ1
2x+14= use distributive property of addition to complete the statement
Answers
Answer:
I think it's 2(x+7).
Step-by-step explanation:
This is distributive function where a number is multiplied from outer value to inner parenthesis values.
I hope this is the right answer.
The endpoints of AB are -4 and 6. Find the coordinate of Point P that partitions the segment in a 2:3 ratio.
Answers
Answer: 0
Step-by-step explanation:
Since it is 10 units total from -4 to 6,
4/10 and 6/10 would give a ratio of 2:3
4 units from -4 would be at 0, which is also 6 units away from the 6
4 units to 6 units equals a ratio of 2:3
Quadrilateral ABCD undergoes a reflection across the x-axis to form quadrilateral A'B'C'D'. The coordinates of A' are (
,
).
The reflected quadrilateral A'B'C'D' is then translated 3 units right and 2 units up to form quadrilateral A"B"C"D". The coordinates of A" are (
,
).
Answers
The coordinates of A'' will be ( -2, 5).
We are given that:
Quadrilateral ABCD is reflected across the x - axis.
We know that, when a refection is done about x-axis, the values of the abscissa x remain identical & the value of ordinate just change their signs:
A(-5,-3) will become A'(-5,+3)
B(-6,-1) will become B'(-6,+1)
C(-3,-1) will become C'(-3,+1)
D(-2,-3) will become D'(-2,+3)
Now, the reflected quadrilateral A'B'C'D' is then translated 3 units right and 2 units up to form quadrilateral A"B"C"D".
So, the coordinates of A'' will become:
( - 5 + 3, 3 + 2)
( -2, 5)
Therefore, we get that, the coordinates of A'' will be ( -2, 5).
Learn more about coordinate here:
https://brainly.com/question/12959377
#SPJ9
Help pls points added
Answers
Answer:
A: (-10, 2)
B: (-5, 2)
C: (-5, 7)
D: (-10, 7)
Step-by-step explanation:
When you reflect over the x axis, you flip the y value, so that what I did.
What is the valur of expression 6 3/4 (-11.5) ?
77 5/8
69 3/4
- 77 5/8
- 69 3/4
I need help
Answers
Step-by-step explanation:
so, this is a multiplication ?
6 3/4 × (-11.5)
let's bring the mixed numbers to full fractions, and then we can easily multiply.
6 3/4 = (6×4 + 3)/4 = (24 + 3)/4 = 27/4
-11.5 = -11 1/2 = (-11×2 - 1)/2 = (-22 - 1)/2 = -23/2
so, the multiplication is
27/4 × -23/2 = 27×-23 / 4×2 = -621/8 =
= (-616 - 5)/8 = (-77×8 - 5)/8 = -77 5/8
Answer:
-77 5/8
Step-by-step explanation:
6 3/4 can be turned into 6.75.
6.75 * -11.5 is -77.625
-77.625 can be simplified into 5/8
Brainliest pls?
what is 3 4 5 6 7 as in mean .
Answers
Answer:
5
Step-by-step explanation:
add the numbers up then divide by how many there are.
3+4+5+6+7=25
25÷5 = 5
What’s the domain and range ??
USE INTERVAL NOTATION.
Only answer if you know!
Answers
Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:Domain and range help us describe the values a graph covers.
Defining Domain and Range
The domain is defined as all the x-values included in a function.The range is defined as all of the y-values included in a function.Remember that the x-values are along the horizontal axis, and the y-values are on the vertical axis.
The function given to us extends infinitely to the left and right as shown by the arrows. Additionally, the graph extends up and down infinitely; thus the range is also infinite.
Interval Notation
Interval notation should be written as (minimum value, maximum value). If the minimum and maximum values are included within the range or domain, then the parentheses should be replaced with brackets. This looks like [included minimum, included maximum]. Since a function cannot actually include infinity, an infinity symbol should never have brackets.
Eventually, this linear function will reach every single x and y-value in existence. So, both axes have a minimum of -∞ and a maximum of ∞. Thus, both the domain and range are (-∞, ∞).
Hint for future problems: all linear functions will have a domain and range of (-∞, ∞).
91-[22{16 divided (39 + 3 of 3-40)}]
Answers
The value of the expression 91 - [ 22 { 16 divided (39 + 3 of 3 - 40 )} ] is 47 by using PEMDAS.
We are given an expression as:
91 - [ 22 { 16 divided (39 + 3 of 3 - 40 )} ]
By the PEMDAS rule, the expression will be:
= 91 - [ 22 {16 ÷ (39 + 9 - 40 ]
= 91 - [ 22 {16 ÷ (8) ]
= 91 - [ 22 {16 ÷ 8} ]
91 - [ 22 {2} ]
= 91 -[ 22 × 2 ]
= 91 - [ 44 ]
= 91 - 44
= 47
Therefore, the value of the expression 91 - [ 22 { 16 divided (39 + 3 of 3 - 40 )} ] is 47 by using PEMDAS.
Learn more about PEMDAS rule here:
https://brainly.com/question/345677
#SPJ9
When the signs are of the integers the same, 1.__________
the integers and copy the 2.) ________ sign. When the signs are
3,) ____________, subtract them and use the sign of the number
with the greater 4) _________. If we add two same numbers with
different signs, then the answer is equal to 5.) ___________.
The sum of two negative integers is a 6. )_________ integer. The
sum of two positive integers is a 7.) ___________ integer.
Answers
The completed statement on the addition and subtraction operations with integers is presented as follows;
When the signs are of the integers of the same sign
1. Add the integers and copy the 2.) integer sign. When the signs are 3) different, subtract them and use the sign of the number with the greater 4) magnitude. If we add two same numbers with different signs, then the answer is equal to 5.) zero. The sum of two negative integer is a 6.) negative integer. The sum of two positive integers is a 7.) positive integer.
How can the operation of adding integers be simplified?The process of adding integers is as follows;
Integers that have the same sign are added together, and the sign of the integers are placed before the result.
The addition of two integers that have different signs involve subtracting the integers and including the sign of the integer with the largest magnitude to the result.
The addition of two the same numbers that have different signs gives the same result as subtracting a number from itself, which is zero.
The sign of the result of the addition or subtraction of two integers of the same is the same as the sign of the integers in the operation.
Learn more about operations with integers here:
https://brainly.com/question/1633188
#SPJ1
a location that is 30 degrees north and 45 degrees west is what of the prime meridian and what of the equator
Answers
A location that is 30 degrees north and 45 degrees west is west of the prime meridian and north of the equator.
A prime meridian refers to an arbitrary meridian which is there in a geographic coordinate system. Here, the longitude is defined as 0°.
A prime meridian and its anti-meridian will together form a great circle in a geographic coordinate system.
The Equator is a circle of latitude, about 40,075 km in circumference, that divides Earth into the Northern and Southern hemispheres.
It is an imaginary line that is located at 0 degrees latitude, and is a halfway between the North and South poles.
Therefore, we get that a location that is 30 degrees north and 45 degrees west is west of the prime meridian and north of the equator.
Learn more about degrees here:
https://brainly.com/question/25716982
#SPJ4
help me plsssss plssss plsssss i will double kiss you
Answers
Answer:
A
Step-by-step explanation:
Sin A = [tex]\frac{opposite}{hypotenuse}[/tex]
Cos A = [tex]\frac{adjacent}{hypotenuse}[/tex]
Answer:
[tex]\text{a.} \quad \sin A=\dfrac{3}{5}, \quad \cos A=\dfrac{4}{5}[/tex]
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angle.O is the side opposite the angle.A is the side adjacent the angle.H is the hypotenuse (the side opposite the right angle).Therefore:
[tex]\implies \sin A =\dfrac{BC}{AB} = \dfrac{3}{5}[/tex]
[tex]\implies \cos A =\dfrac{AC}{AB} = \dfrac{4}{5}[/tex]
what’s 17x3-11y2-14y3
Answers
Reason:
Subtract 14x^3 from 17x^3
Answer:
3x^3-11y^2
Step-by-step explanation:
17x^3 -11y^2 -14x^3
collect like terms
17x^3 -14x^3 =3x^3
3x^3-11y^2
I hope it helps.
A stack of Sunday newspapers sits on a skid 3" off the ground.
Each newspaper is 13" thick.
a. How high is the stack if there are n newspapers in it?
b. If the top of the stack is 3' high, about how many newspapers
are in the stack?
Answers
Answer: a. 3+13n
b. About 3 newspapers
Step-by-step explanation:
a. T=total thickness of newspapers on a skid in inches
T=3+13n
b. 3'=3 ft
1 ft=12 inches
3 ft=3*12 inches
3 ft=36 inches
36=3+13n
13n=33
n=2.54 ==> About 3 newspapers
(2x−6)(x−2) multiply
Answers
Step-by-step explanation:
Solving steps
(2x-6)×(x-2)
Multiply
2x×x-2x×2-6x-6x 2
Calculate Multiply
2x²-4x-6x+12
Collect like terms
Solution
2x²- 10x + 12
Four dice are rolled sequentially. What is the probability that the first die shows six and the other dice show an odd number? IN FRACTIONS!
Answers
Answer:
1/48
Step-by-step explanation:
The total number of different outcomes when rolling 4 dice is
6 × 6 × 6 × 6 = 1296
The possible number of outcomes of rolling a 6 followed by 3 odd numbers is
1 × 3 × 3 × 3 = 27
p(6 followed by 3 odd numbers) = 27/1296 = 1/48
help pls no clue where to start
Answers
Answer:
[tex]P_{rofit}=13x-50\\C_{ost}(70)=960\\P_{rofit}(70)=860\\C_{ost}(100)=1350\\P_{rofit}(100)=1250\\For\ a\ profit\ of\ \$1100\ one\ must\ sell\ 89\ stuffed\ animals.[/tex]
Step-by-step explanation:
I would suggest starting with 1 and working to 4, as it is set up for you like that.
I would start by writing down what you know, then what you need as follows:
[tex]Givens:\\ C_{ost}=13x+50;\\ R_{evenue}=36x;\\P_{rofit}=R_{evenue}-C_{ost};\\ x=N_{umber\ of\ animals}\\[/tex]
[tex]Find:\\1.\ Profit\ equation\\2a.\ C_{ost}\ to\ make\ 70\ animals\\2b.\ P_{rofit}\ from\ selling\ 70\ animals\\3a.\ C_{ost}\ to\ make\ 100\ animals\\3b.\ P_{rofit}\ from\ selling\ 100\ animals\\4.\ N_{umber}\ of\ animals\ needed\ to\ produce\ P_{rofit}\ of\ \$1100[/tex]
Now you can read it easier. Given that Profit is Revenue minus Cost, plug the equations for Cost and Revenue into the Profit equation as follows:
[tex]P_{rofit}=36x-(13x+50)\\NOTE:\ Do\ NOT\ forget\ to\ put\ the\ C_{ost}\ equation\ in\ parenthesis\ as\ you\ \\must\ subtract\ the\ entire\ C_{ost}.\\\\Distribute\ the\ negative:\ P_{rofit}=36x-13x-50\\Combine\ like\ terms:\ P_{rofit}=13x-50[/tex]
With the Profit equation, it is now easier to solve 2b, 3b, and 4.
[tex]C_{ost}\ for\ 70: C_{ost}=13(70)+50=(700+210)+50\\NOTE:\ I\ used\ the\ fact\ that\ 13*70=(10+3)*70=10*70+3*70\\C_{ost}=910+50=960\\This\ could\ also\ be\ written\ more\ clearly\ as\ C_{ost}(70)=960\\\\P_{rofit}(70) = 13(70)-50\\P_{rofit}(70)=(700+210)-50\\P_{rofit}(70)=910-50\\P_{rofit}(70)=860\\\\C_{ost}(100)=13(100)+50\\C_{ost}(100)=(1300)+50\\C_{ost}(100)=1350\\\\P_{rofit}(100)=13(100)-50\\P_{rofit}(100)=(1300)-50\\P_{rofit}(100)=1250\\[/tex]
Problem 4 will involve using the (now) known amount for profit, $1100 to find the unknown number of animals. This will involve a little bit more "algebra" compared to the prior questions.
[tex]P_{rofit}(x)=1100=13x-50\\1100=13x-50\\[/tex]
Because 13x - 50 is 1100, 13x will be 1100 + 50, just as
[tex]5*2+10 = 20\\5*2=20-10\\[/tex]
So, add 50 to both sides:
[tex]1100+50=13x-50+50\\1150=13x\\[/tex]
Because 13x is 1150, x will be 1150÷13, just as
[tex]5*2=10\\5=\frac{10}{2}[/tex]
So, divide 13 from both sides:
[tex]\frac{1150}{13}=\frac{13x}{13}\\\\\frac{1150}{13}=x[/tex]
Because 1150/13 is not an integer, use a calculator, or simplify the improper fraction to obtain...
x=88.5 (Approximately)
But, because you cannot sell half an animal, you would have to sell 89 in order to profit $1100, for bonus points, what is the actual profit accrued by selling 89 animals?
8
k
-2
-1
0
1
b=
2
RETRY✔
f(x) = -x² + x + 6
a
4
b
6
10
Answers
The missing values are a = 0, b= 6 and c=4.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
We have function,
f(x) = -x² + x + 6
At x= -2
f(-2) = -(-2)² + (-2) + 6 = -4 -2 + 6= 0
At x = 0
f(0) = -0² + 0 + 6= 6
At x = 2
f(2) = -2² + 2 +6 = -4 + 8= 4
Learn more about Function here:
https://brainly.com/question/12431044
#SPJ5
Determine whether the following statement is true or false. Explain.
The graph of y = |x-2|- 2 is a translation two units to the right and two units upward of the graph of y = |x|.
Choose the correct answer below.
A. True, because the graph of y = f(x - h) + k is the translation of the graph of y = f(X) |k| units upward if k= 0 or downward if k < 0, and h units to the right if h> 0 or to the
left if h < 0.
B. True, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) In| units upward if h = 0 or downward if h < 0, and k units to the right if k> O or to the
left if k < O
C. False, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) |k| units to the right if k>0 or to the left if k < 0, and h units upward if h downward if h < 0.
D. False, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) h units to the right if h > 0 or to the left if h < 0, and k units upward if k>downward if k < 0.
Answers
Answer:
Determine whether the following statement is true or false. Explain.
The graph of y = |x-2|- 2 is a translation two units to the right and two units upward of the graph of y = |x|.
Choose the correct answer below.
A. True, because the graph of y = f(x - h) + k is the translation of the graph of y = f(X) |k| units upward if k= 0 or downward if k < 0, and h units to the right if h> 0 or to the
left if h < 0.
B. True, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) In| units upward if h = 0 or downward if h < 0, and k units to the right if k> O or to the
left if k < O
C. False, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) |k| units to the right if k>0 or to the left
89. Philip solved the following problem incorrectly. Explain his mistake.
1659
x 21
1659
+3318
4977
Answers
Philip's mistake is he did not add zero at ten's place.
When the multiplication is performed with two or more digits in the bottom number, zeroes are added as per the position. We see that in number 21, one is at one's place and 2 is at ten's place. Hence, when multiplying the digit 2 with the number 1659, we will add zero at one's place.
Performing the correct multiplication -
1659
× 21
1659
+33180
The result of multiplication will be the sum of numbers 1659 and 33180.
Result = 34,839
Therefore, the multiplication of the numbers will give result 34,839. Hence, the mistake is not keeping zero at one's place, while performing multiplication.
Learn more about multiplication -
https://brainly.com/question/14416366
#SPJ4
if \mathbf{x}x is an optimal solution to a linear program pp, then \mathbf{x}x is a vertex of pp's feasible region.
Answers
Yes, it is true that if "x" is an optimal solution to a linear programming problem, then it is a vertex of the feasible region.
Linear programming (LP) is one of the most basic methods of optimization. By making a few simplifying assumptions, it can assist you in solving some highly complicated optimization issues.Linear programming is a basic approach that uses linear functions to represent complicated connections and then finds the optimum spots.Linear programming is used to find the best solution to a problem given certain limitations. In linear programming, we transform a real-world issue into a mathematical model. It consists of an objective function, linear inequalities, and constraints.A graphical technique entails constructing a collection of linear inequalities that are constrained. The disparities are then plotted on an X-Y plane. When we plot all of the inequalities on a graph, the intersecting region provides us with a viable region. The viable region describes all of the values that our model may take. It also provides us with the best solution.At the point of intersection, when the constraints are active, the best viable solution is found. This signifies that the intersection of the equations provides the best answer.
To learn more about linear programming, visit :
https://brainly.com/question/15417573
#SPJ4
what is the simplest form of 2/4 divide by 4/9
Answers
Answer:
it 9/ 8
Step-by-step explanation:
2/4× 9/4
18/16
9/8
The radius of a circle measures 16 yd.. What is the circumference of the circle? Use 3.14 for pi , and do not round your answer. Be sure to include the correct unit in your answer.
Answers
C=2πr=2·π·16≈ 100.53096
Anyone know this?????
Answers
Answer:
Final answer: P=(1,5)
Step-by-step explanation:
The line APB is a line such that AP/PB= 1/3. From the points A and B that we have we can find the distance between those points using the formula d= [(y2-y1)^2=(x2-x1)^2]^1/2
d= 4 (13)^(1/2)
Now the ratio is 1:3. AP= sq rt(13) and PB= 3 sq rt(13)
Using mid point formula the mid point of AB (say Q) = [(-1+7)/2,(2+14)/2]= (3,8).
Hence the mid point of AQ is P which can found out again using the mid point formula
P= [(-1+3)/2,(2+8)/2]= (1,5)