Question

Help please? if JKhas endpoints J(-2,3) and k(6,5), and LN has endpoints L(0,7) and N(4,1), then JK and LN have the same midpoint. 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

In this item, it is assumed that what is asked is that if the statement is TRUE or FALSE.

Part A:
The coordinates of the midpoint of the given endpoints of the line is equal to half of the sum of the coordinates.

Line JK
abscissa = (-2 + 6) / 2 = 2
ordinate = (3 + 5) / 2 = 4
Midpoint is (2, 4)

Line LN
abscissa = (0 + 4) / 2 = 2
ordinate = (7 + 1) / 2 = 4
Midpoint is (2, 4)

Hence, the statement is TRUE.

Part B:
abscissa = (-8 + 4)/ 2= -2
ordinate = (1 + 5) / 2 = 3

Midpoint = (-2, 3)

Substituting the point to the given equation,
y = - x + 1
3 = -(-2) + 1 = 3

Thus, all statement is TRUE.