Question

What are the coordinates of point Q if the midpoint of line QR is (9, -4) and the coordinate of point R is (-10, 78) ? Show your work or explain your thinking.

Answer 1

The coordinates of point Q are (28, -38).

Step-by-step explanation:

To find the coordinates of point Q, we can first find the midpoint of line QR using the coordinates of point R and the given midpoint coordinate. The midpoint coordinates (9, -4) can be found by taking the average of the x-coordinates and the average of the y-coordinates. So, we have:

x-coordinate of Q = (x-coordinate of R + x-coordinate of P) / 2 = (-10 + x-coordinate of P) / 2 = 9

Solving for x-coordinate of P, we get: x-coordinate of P = 2 * 9 + 10 = 28

y-coordinate of Q = (y-coordinate of R + y-coordinate of P) / 2 = (78 + y-coordinate of P) / 2 = -4

Solving for y-coordinate of P, we get: y-coordinate of P = 2 * (-4) - 78 = -38

Therefore, the coordinates of point Q are (28, -38).