Question

the midpoint of $overline{rs}$ is $m(5, 5)$. one endpoint is $s(4, 6)$. find the coordinates of the other endpoint $r$. write the coordinates as decimals or integers. $r = (square,square)$

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 $R=(x,y)$ and $S=(4,6)$ and $M=(5,5)$.

Step2: Solve for x - coordinate

We know that $\frac{x + 4}{2}=5$. Cross - multiply: $x + 4=10$. Then subtract 4 from both sides: $x=10 - 4=6$.

Step3: Solve for y - coordinate

We know that $\frac{y + 6}{2}=5$. Cross - multiply: $y+6 = 10$. Then subtract 6 from both sides: $y=10 - 6 = 4$.

Answer:

$(6,4)$