Question

c. you can graph the segments to find the point where they intersect. do the segments intersect at one of the midpoints? explain your reasoning. turn and talk: if $overline{cd}$ has an endpoint $c(4, - 6)$ and the midpoint is $m(- 2,6)$, what are the coordinates of the endpoint $d$? explain how you found the 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 $C(x_1,y_1)=(4,-6)$ and $M(x_m,y_m)=(-2,6)$, and $D(x_2,y_2)$ be the unknown endpoint.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, we have $-2=\frac{4 + x_2}{2}$. Multiply both sides by 2: $-4 = 4+x_2$. Then subtract 4 from both sides: $x_2=-8$.

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the values, we have $6=\frac{-6 + y_2}{2}$. Multiply both sides by 2: $12=-6 + y_2$. Then add 6 to both sides: $y_2 = 18$.

Answer:

The coordinates of endpoint $D$ are $(-8,18)$.