Question

If GH has endpoints G(-8, 1) and H(4, 5), then the midpoint M of GH lies on the line y=-x+1

Answer 1

The midpoint of GH is (-2, 3), and that point satisfies the equation because

3 = -(-2) + 1
3 = 2 + 1
3 = 3

Answer 2

Explanation:

If GH has a midpoint M(x, y) then we have to determine whether midpoint M lies on the given line y = -x + 1

Since coordinates of G and H are (-8, 1) and (4, 5) so coordinates of the midpoint M will be

x =
`((-8+4))/(2)` = -2

and y coordinates of point M will be

y =
`((1+5))/(2)` = 3

Therefore point M is (-2, 3).

Now we plug in the values of x and y in the given equation.

3 = -(-2) + 1

3 = 3

Hence it is proved that the midpoint M of segment GH will lie on the line y = -x + 1