The ordered pair for Y is (-4,-2)
Step-by-step explanation:
Given
X(-2,3)
Z(-6,-7)
As Y is the mid-point of XZ, it will divide Xz in two equal segments. Y is the mid-point of the segment.
Let (x_Y, y_Y) be the coordinates of the mid-point
Then
![(x_Y, y_Y) = (\frac{x_1+_2}{2} , \frac{y_1+y_2}{2})](https://tex.z-dn.net/?f=%28x_Y%2C%20y_Y%29%20%3D%20%28%5Cfrac%7Bx_1%2B_2%7D%7B2%7D%20%2C%20%5Cfrac%7By_1%2By_2%7D%7B2%7D%29)
Putting the values
![=(frac{-2-6}{2} , \frac{3-7}{2})\\=(\frac{-8}{2} , \frac{-4}{2})\\=(-4, -2)](https://tex.z-dn.net/?f=%3D%28frac%7B-2-6%7D%7B2%7D%20%2C%20%5Cfrac%7B3-7%7D%7B2%7D%29%5C%5C%3D%28%5Cfrac%7B-8%7D%7B2%7D%20%2C%20%5Cfrac%7B-4%7D%7B2%7D%29%5C%5C%3D%28-4%2C%20-2%29)
Hence,
The ordered pair for Y is (-4,-2)
Keywords: Coordinate geometry, Mid-point
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