Question

the midpoint of $overline{pq}$ is $m=(5, - 2)$. one endpoint is $p=(2,3)$. find the coordinates of the other endpoint, $q$.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1 = 2,y_1 = 3$ and $M(5,-2)$.

Step2: Solve for $x_2$

We have $\frac{2 + x_2}{2}=5$. Multiply both sides by 2: $2 + x_2=10$. Then subtract 2 from both sides: $x_2=10 - 2=8$.

Step3: Solve for $y_2$

We have $\frac{3 + y_2}{2}=-2$. Multiply both sides by 2: $3 + y_2=-4$. Then subtract 3 from both sides: $y_2=-4 - 3=-7$.

Answer:

$Q=(8,-7)$