Question

tu has a mid - point at m(-2, -14.5). point t is at (-2, -11). find the coordinates of point u. write the coordinates as decimals or integers. u = ( )

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 $T(x_1,y_1)=(-2,-11)$ and $U(x_2,y_2)$. The mid - point $M(-2,-14.5)$.

Step2: Solve for the x - coordinate of U

We know that $\frac{x_1 + x_2}{2}=-2$. Substitute $x_1=-2$ into the equation: $\frac{-2 + x_2}{2}=-2$. Multiply both sides by 2: $-2+x_2=-4$. Add 2 to both sides: $x_2=-2$.

Step3: Solve for the y - coordinate of U

We know that $\frac{y_1 + y_2}{2}=-14.5$. Substitute $y_1 = - 11$ into the equation: $\frac{-11 + y_2}{2}=-14.5$. Multiply both sides by 2: $-11+y_2=-29$. Add 11 to both sides: $y_2=-18$.

Answer:

$(-2,-18)$