Question

b is the midpoint of $overline{ac}$. a has coordinates (-8, -15), and b has coordinates (6, 4). find the coordinates of c.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $A(x_1,y_1)$ and $C(x_2,y_2)$ with mid - point $B(x_m,y_m)$ is $x_m=\frac{x_1 + x_2}{2}$ and $y_m=\frac{y_1 + y_2}{2}$. Here $x_1=-8,y_1=-15,x_m = 6,y_m = 4$.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$, so $6=\frac{-8 + x_2}{2}$. Multiply both sides by 2: $12=-8 + x_2$. Then add 8 to both sides: $x_2=12 + 8=20$.

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$, so $4=\frac{-15 + y_2}{2}$. Multiply both sides by 2: $8=-15 + y_2$. Then add 15 to both sides: $y_2=8 + 15=23$.

Answer:

$(20,23)$