Question

Question 5 (20 points)

The midpoint M and one endpoint of AB are given. Find the coordinates of the other endpoint.
A(-8,4) and M(5,-9).
a
(10,-22)
b
(18,-8)
c
(18,-22)
d
(6,-22)

Answer 1

Let B be the other endpoint of AB.

We know that the midpoint M of AB has coordinates (5, -9), which means that the average of the x-coordinates of A and B is 5, and the average of the y-coordinates of A and B is -9:

• ( x_A + x_B ) / 2 = 5
• ( y_A + y_B ) / 2 = -9

Substituting the coordinates of point A (-8, 4), we can solve for the x-coordinate of point B:

• ( -8 + x_B ) / 2 = 5

Simplifying the equation, we get:

• -8 + x_B = 10
• x_B = 18

Now, substituting the same coordinates of point A and the y-coordinate of midpoint M (-9), we can solve for the y-coordinate of point B:

• ( 4 + y_B ) / 2 = -9

Simplifying the equation, we get:

• 4 + y_B = -18
• y_B = -22

Therefore, the coordinates of point B are (18, -22).