Question

the midpoint of $overline{qr}$ is $m(45, 58.5)$. one endpoint is $r(64, 46)$. find the coordinates of the other endpoint $q$. write the coordinates as decimals or integers. $q = ( , )$

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 $Q=(x,y)$ and $R=(64,46)$ and $M=(45,58.5)$.

Step2: Solve for x - coordinate of Q

We know that $\frac{x + 64}{2}=45$. Multiply both sides by 2: $x + 64=90$. Then subtract 64 from both sides: $x=90 - 64=26$.

Step3: Solve for y - coordinate of Q

We know that $\frac{y + 46}{2}=58.5$. Multiply both sides by 2: $y + 46 = 117$. Then subtract 46 from both sides: $y=117-46 = 71$.

Answer:

$(26,71)$