Question

the midpoint of $overline{cd}$ is $m(5, 3)$. one endpoint is $d(2, 5)$. find the coordinates of the other endpoint $c$. write the coordinates as decimals or integers. $c =$

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 $C=(x,y)$ and $D=(2,5)$ and $M=(5,3)$.

Step2: Solve for x - coordinate

We know that $\frac{x + 2}{2}=5$. Multiply both sides by 2: $x + 2=10$. Then subtract 2 from both sides: $x=10 - 2=8$.

Step3: Solve for y - coordinate

We know that $\frac{y + 5}{2}=3$. Multiply both sides by 2: $y + 5=6$. Then subtract 5 from both sides: $y=6 - 5 = 1$.

Answer:

$C=(8,1)$