Question

the midpoint of $overline{uv}$ is $m(8, 2.5)$. one endpoint is $v(5, 3)$. find the coordinates of the other endpoint $u$. write the coordinates as decimals or integers. $u = (square,square)$

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 $U=(x,y)$ and $V=(5,3)$ and $M=(8,2.5)$.

Step2: Solve for x - coordinate

We know that $\frac{x + 5}{2}=8$. Multiply both sides by 2: $x + 5=16$. Then subtract 5 from both sides: $x=16 - 5=11$.

Step3: Solve for y - coordinate

We know that $\frac{y + 3}{2}=2.5$. Multiply both sides by 2: $y+3 = 5$. Then subtract 3 from both sides: $y=5 - 3=2$.

Answer:

$(11,2)$