Answer:
Since, the coordinates of the midpoint of line GH are M(\frac{-13}{2}, -6)(
2
−13
,−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)(x
1
,y
1
) and (x_2, y_2)(x
2
,y
2
) is given by the formula (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})(
2
x
1
+x
2
,
2
y
1
+y
2
) .
Here, The endpoint G is (-4,1) So, x_1 = -4 , y_1=1x
1
=−4,y
1
=1
Let the endpoint H be (x_2,y_2)(x
2
,y
2
)
The midpoint coordinate M is (\frac{-13}{2}, -6)(
2
−13
,−6) .
So, \frac{-13}{2} = \frac{-4+x_2}{2}
2
−13
=
2
−4+x
2
{-13} = {-4+x_2}−13=−4+x
2
{-13}+4 = {x_2}−13+4=x
2
{x_2}=9x
2
=9
Now, -6 = \frac{1+y_2}{2}−6=
2
1+y
2
-12 = {1+y_2}−12=1+y
2
y_2= -13y
2
=−13
So, the other endpoint H is (-9,-13).
