Question

Show that the statement is true. If GH has endpoints G(−2, 1) and H(4, −1), then the midpoint M of GH lies on the line y = −x + 1.

The midpoint M is ( , ). The midpoint does not lie or lies on the line y = −x + 1 since its coordinates satisfy or do not satisfy the equation.

Answer 1

midpoint = (x1 + x2) / 2, (y1 + y2)/2
(-2,1)....x1 = -2 and y1 = 1
(4,-1)...x2 = 4 and y2 = -1
time to sub
m = (-2 + 4) / 2 , (1 + (-1) / 2
m = (2/2), (0/2)
m = (1,0) <==

y = -x + 1.....(1,0)...x = 1 and y = 0
0 = -1 + 1
0 = 0 (correct)

so the midpoint  M (1,0) lies on the line since its coordinates satisfy the equation <===