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)

The coordinates of the other endpoint are ( , )

Answer 1

Since, the coordinates of the midpoint of line GH are M
`((-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
`((x_1+x_2)/(2),(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
`((-13)/(2), -6)`.

So,
`(-13)/(2) = (-4+x_2)/(2)`

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

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

`{x_2}=9`

Now,
`-6 = (1+y_2)/(2)`

`-12 = {1+y_2}`

`y_2= -13`

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