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

(18,-22)

Explanation:

We can use the midpoint formula to find the coordinates of the other endpoint of AB. The midpoint formula is:

• M = ((x1 + x2)/2, (y1 + y2)/2)

where M is the midpoint of AB, (x1, y1) are the coordinates of one endpoint of AB (in this case, A), and (x2, y2) are the coordinates of the other endpoint of AB (which we are trying to find).

Substituting the given values:

• M = (5, -9)
• A = (-8, 4)
• M = ((x1 + x2)/2, (y1 + y2)/2)
• (5, -9) = ((-8 + x2)/2, (4 + y2)/2)

Solving this system of equations for x2 and y2, we get:

-8 + x2 = 2(5) = 10 (multiplying both sides by 2)4 + y2 = 2(-9) = -18 (multiplying both sides by 2)

Adding 8 to both sides of the first equation, and subtracting 4 from both sides of the second equation, we get:

• x2 = 10 + 8 = 18
• y2 = -18 - 4 = -22

Therefore, the coordinates of the other endpoint of AB are (18, -22).