Question

the midpoint of $overline{cd}$ is $m = (-4,0)$. one endpoint is $c = (-8,2)$. find the coordinates of the other endpoint, $d$.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $C=(x_1,y_1)=(-8,2)$ and $D=(x_2,y_2)$, and $M=(-4,0)$.

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: $x_2 = 0$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=0$. Substitute $y_1 = 2$ into the equation: $\frac{2 + y_2}{2}=0$. Multiply both sides by 2: $2 + y_2=0$. Then subtract 2 from both sides: $y_2=-2$.

Answer:

$(0,-2)$