Question

The midpoint of bar (PQ) is M=(1,0). One endpoint is P=(-6,8). Find the coordinates of the other endpoint, Q.

Answer 1

Using the midpoint formula, the coordinates of the other endpoint Q of the line segment PQ are calculated to be (8, -8).

Step-by-step explanation:

To find the coordinates of the other endpoint Q of the line segment PQ with midpoint M=(1,0) and one endpoint P=(-6,8), you can use the midpoint formula. The midpoint M is the average of the x-coordinates and the y-coordinates of points P and Q. Mathematically:

M = ((xP + xQ)/2, (yP + yQ)/2)

We can set up the equations:

1. (-6 + xQ)/2 = 1
2. (8 + yQ)/2 = 0

Solve for xQ and yQ by multiplying both sides by 2 and then adding or subtracting the coordinates of P:

1. xQ = 2(1) + 6 = 8
2. yQ = 2(0) - 8 = -8

The coordinates of endpoint Q are (8, -8).