Question

the mid - point of $overline{uv}$ is $m(4.5, - 10.5)$. one endpoint is $v(9, - 19)$. find the coordinates of the other endpoint $u$. write the coordinates as decimals or integers. $u=(spacespace,spacespace)$

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 $V=(9,-19)$ and $M=(4.5,-10.5)$.

Step2: Solve for x - coordinate of U

We have $\frac{x + 9}{2}=4.5$. Multiply both sides by 2: $x + 9=9$. Then subtract 9 from both sides: $x=9 - 9=0$.

Step3: Solve for y - coordinate of U

We have $\frac{y+( - 19)}{2}=-10.5$. Multiply both sides by 2: $y-19=-21$. Then add 19 to both sides: $y=-21 + 19=-2$.

Answer:

$(0,-2)$