Question

Estefani‘s house is at point E (3,-2) and Jasmin’s house is at point J (-5,3). Jasmin’s house is the Mid-point of Estefani’s house and Preston’s house. Give the y-coordinate of Preston’s house.

Answer 1

The formula for midpoint is

($\frac{x_{1}+x_{2}}{2}$, $\frac{y_{1}+y_{2}}{2}$)

Look at the image below to see the line segment of Estefani's (A), Jasmin's (M), and Preston's (B) houses. Keep in mind that the segment shown below is not accurate in regards to how the line segment formed by Estefani's, Jasmin's, and Preston's houses. It is simply there so you can picture the segment better.

In this case:

$x_{1} =3\\x_{2} =unknown\\y_{1} =-2\\y_{2} =unknown$

^^^Plug in these number into the formula given above...

($\frac{3+x}{2}$, $\frac{-2 + y}{2}$)

To find what x is (a coordinate of Preston's house) you must take the x-value part of the midpoint equation ($\frac{3+x}{2}$) and set it equal to the x-value of the midpoint (-5). Then you must solve for x:

$\frac{3+x}{2}$ = -5

3 + x = -5 * 2

3 + x = -10

x = -10 - 3

x = -13

To find what y is (a coordinate of Preston's house) you must take the  y-value part of the midpoint equation($\frac{-2 + y}{2}$) and set it equal to the y-value of the midpoint (3). Then you must solve for y:

$\frac{-2 + y}{2}$ = 3

-2 + y = 3 * 2

-2 + y = 6

y = 6 + 2

y = 8

The coordinate of Preston's house is:

(-13, 8)

Hope this helped!

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