Question

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

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $P=(3,-3)$ and $M=(-2,-5)$. Let the coordinates of $Q$ be $(x,y)$.

Step2: Solve for the x - coordinate of Q

We know that $\frac{3 + x}{2}=-2$. Cross - multiply: $3 + x=-4$. Then subtract 3 from both sides: $x=-4 - 3=-7$.

Step3: Solve for the y - coordinate of Q

We know that $\frac{-3 + y}{2}=-5$. Cross - multiply: $-3 + y=-10$. Then add 3 to both sides: $y=-10 + 3=-7$.

Answer:

$(-7,-7)$