Question

If Q is the midpoint of PR, find the coordinates of the endpoint R. P(11,-2) and Q(4,3).

A) R(17, 8)
B) R(18, 7)
C) R(13, -7)
D) R(8, 4)

Answer 1

To find the unknown endpoint R, the midpoint formula is manipulated to solve for the other endpoint's coordinates from the known values of endpoint P and midpoint Q. The coordinates for R are (-3, 8).

Step-by-step explanation:

To find the coordinates of endpoint R given that Q is the midpoint of PR, and you have the coordinates of P (11, -2) and Q (4, 3), you can use the midpoint formula. The midpoint formula is (x1 + x2)/2, (y1 + y2)/2 where (x1, y1) are the coordinates of one endpoint, and (x2, y2) are the coordinates of the midpoint. To find x2 and y2 for the other endpoint, you'll rearrange the formula:

• x2 = 2x(midpoint) - x1
• y2 = 2y(midpoint) - y1

By substituting in our known values, we get:

• x2 = 2(4) - 11 = 8 - 11 = -3
• y2 = 2(3) - (-2) = 6 + 2 = 8

The coordinates for R are therefore (-3, 8).