If (-2,3) is the midpoint of segment PQ and the coordinates of P are (-8,5) find the coordiantes of Q?

Question

If (-2,3) is the midpoint of segment PQ and the coordinates of P are (-8,5) find the coordiantes of Q?

Answer 1

Think of the projections of your segment on the two coordinate axes.

On the horizontal axis we have the projection

P = -8      midpoint = -2       Q = ?

Because the distance from P to the midpoint is the same as the distance from the midpoint to Q, we see that Q must be 6 units to the right of the midpoint, that is, the horizontal coordinate of Q is 4.

On the vertical axis, we have the projection

P = 5

midpoint = 3

Q = ?

By the same reasoning, we see that the vertical coordinate of Q is 2 units below the midpoint, that is, Q = 1.

ANSWER: The coordinates of Q are (4,2).