Question

the midpoint of $overline{cd}$ is $m = (-4, -2)$. one endpoint is $c = (-7, 3)$. 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 $C=(x_1,y_1)=(-7,3)$ and $D=(x_2,y_2)$, and $M=(-4,-2)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-4$. Substitute $x_1=-7$ into the equation: $\frac{-7 + x_2}{2}=-4$. Multiply both sides by 2: $-7 + x_2=-8$. Then add 7 to both sides: $x_2=-8 + 7=-1$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=-2$. Substitute $y_1 = 3$ into the equation: $\frac{3 + y_2}{2}=-2$. Multiply both sides by 2: $3 + y_2=-4$. Then subtract 3 from both sides: $y_2=-4 - 3=-7$.

Answer:

$D=(-1,-7)$