Question

the midpoint of $overline{pq}$ is $m = (-4,1)$. one endpoint is $p=(-8, -6)$. 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 $x_1=-8,y_1 = - 6$, and $M(-4,1)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-4$. Substitute $x_1=-8$ into the equation: $\frac{-8 + x_2}{2}=-4$. Multiply both sides by 2: $-8 + x_2=-8$. Then add 8 to both sides, we get $x_2 = 0$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=1$. Substitute $y_1=-6$ into the equation: $\frac{-6 + y_2}{2}=1$. Multiply both sides by 2: $-6 + y_2=2$. Then add 6 to both sides, we get $y_2=8$.

Answer:

$(0,8)$