To find the endpoint of the line segment with endpoint Z(–21, 15) and midpoint M(–13, 29), we need to use the midpoint formula, which states that the midpoint of a line segment is the average of its endpoints:
Midpoint formula: (x1 + x2)/2, (y1 + y2)/2 = (x, y)
We can plug in the values we know:
(x1 + x2)/2 = -13
(y1 + y2)/2 = 29
x1 = -21
y1 = 15
Solving for x2 and y2:
x2 = -2x1 - 26 = -2(-21) - 26 = 16
y2 = 2y1 - 18 = 2(15) - 18 = 12
Therefore, the endpoint of the line segment with endpoint Z(–21, 15) and midpoint M(–13, 29) is E(16, 12).