Question

find the coordinates of the missing endpoint if b is the midpoint of $overline{ac}$. c(-6, -2), b(-3, -5) a( )

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 $y_m=\frac{y_1 + y_2}{2}$. We know $x_2=-6,y_2 = - 2,x_m=-3,y_m=-5$.

Step2: Solve for $x_1$

Using $x_m=\frac{x_1 + x_2}{2}$, substitute the known values: $-3=\frac{x_1-6}{2}$. Multiply both sides by 2: $-6=x_1 - 6$. Add 6 to both sides: $x_1=0$.

Step3: Solve for $y_1$

Using $y_m=\frac{y_1 + y_2}{2}$, substitute the known values: $-5=\frac{y_1-2}{2}$. Multiply both sides by 2: $-10=y_1 - 2$. Add 2 to both sides: $y_1=-8$.

Answer:

$(0,-8)$