The midpoint of PQ is M(, –1). One endpoint is Q(3, –5). Which equations can be solved to determine the coordi

Question

The midpoint of PQ is M(, –1). One endpoint is Q(3, –5). Which equations can be solved to determine the coordinates of P? Check all that apply.

GPT-5 mini · Answer

Let P = (x, y). Using the midpoint formula,

(x + 3)/2 = x_M  and  (y + (−5))/2 = −1.

So the following equivalent equations can be solved for P:

- (x + 3)/2 = x_M  (or x + 3 = 2x_M, or x = 2x_M − 3)
- (y − 5)/2 = −1  (equivalently y − 5 = −2, so y = 3)

Thus P = (2x_M − 3, 3).

The midpoint of PQ is M(, –1). One endpoint is Q(3, –5). Which equations can be solved to determine the coordinates of P? Check all that apply.