Question

The coordinates of the midpoint of line GH are M(−132,−6) M ( − 13/2 , − 6 ) and the coordinates of one endpoint are G(−4, 1)

Answer 1

Since, the coordinates of the midpoint of line GH are M$(\frac{-13}{2}, -6)$.

The coordinates of endpoint G are (-4,1)

We have to determine the coordinates of endpoint H.

The midpoint of the line segment joining the points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.

Here, The endpoint G is (-4,1) So, $x_1 = -4 , y_1=1$

Let the endpoint H be $(x_2,y_2)$

The midpoint coordinate M is $(\frac{-13}{2}, -6)$.

So, $\frac{-13}{2} = \frac{-4+x_2}{2}$

${-13} = {-4+x_2}$

${-13}+4 = {x_2}$

${x_2}=9$

Now, $-6 = \frac{1+y_2}{2}$

$-12 = {1+y_2}$

$y_2= -13$

So, the other endpoint H is (-9,-13).