Question

the midpoint of $overline{uv}$ is $m(13, 11.5)$. one endpoint is $v(9, 20)$. find the coordinates of the other endpoint $u$. write the coordinates as decimals or integers.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $U(x_1,y_1)$ and $V(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $M(13,11.5)$ and $V(9,20)$.

Step2: Find the x - coordinate of U

We know that $\frac{x_1+9}{2}=13$. Cross - multiply: $x_1 + 9=26$. Then $x_1=26 - 9=17$.

Step3: Find the y - coordinate of U

We know that $\frac{y_1 + 20}{2}=11.5$. Cross - multiply: $y_1+20 = 23$. Then $y_1=23 - 20 = 3$.

Answer:

$(17,3)$