Question

the midpoint of $overline{pq}$ is $m(84.5, 54)$. one endpoint is $p(75, 17)$. find the coordinates of the other endpoint $q$. write the coordinates as decimals or integers. $q = ( square, square )$

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $M(84.5,54)$ and $P(75,17)$, we can set up equations.
Let $x_1 = 75,y_1 = 17$, and the coordinates of $Q$ be $(x_2,y_2)$. Then $\frac{x_1 + x_2}{2}=84.5$ and $\frac{y_1 + y_2}{2}=54$.

Step2: Solve for $x_2$

We have $\frac{75 + x_2}{2}=84.5$. Multiply both sides by 2: $75+x_2 = 84.5\times2=169$. Then subtract 75 from both sides: $x_2=169 - 75=94$.

Step3: Solve for $y_2$

We have $\frac{17 + y_2}{2}=54$. Multiply both sides by 2: $17 + y_2=54\times2 = 108$. Then subtract 17 from both sides: $y_2=108 - 17 = 91$.

Answer:

$(94,91)$