The midpoint of the line segment with endpoints at the given coordinates (-6,6) and (-3,-9) is [tex]\left(\frac{-9}{2}, \frac{-3}{2}\right)[/tex]
Solution:
Given, two points are (-6, 6) and (-3, -9)
We have to find the midpoint of the segment formed by the given points.
The midpoint of a segment formed by [tex]\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \text { and }\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)[/tex] is given by:
[tex]\text { Mid point } \mathrm{m}=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
[tex]\text { Here in our problem, } x_{1}=-6, y_{1}=6, x_{2}=-3 \text { and } y_{2}=-9[/tex]
Plugging in the values in formula, we get,
[tex]\begin{array}{l}{m=\left(\frac{-6+(-3)}{2}, \frac{6+(-9)}{2}\right)=\left(\frac{-6-3}{2}, \frac{6-9}{2}\right)} \\\\ {=\left(\frac{-9}{2}, \frac{-3}{2}\right)}\end{array}[/tex]
Hence, the midpoint of the segment is [tex]\left(\frac{-9}{2}, \frac{-3}{2}\right)[/tex]
