Question

uv has a mid - point at m(8.5, 1.5). point u is at (8, 16). find the coordinates of point v. write the coordinates as decimals or integers. v = ( )

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 $U=(x_1,y_1)=(8,16)$ and $V=(x_2,y_2)$, and $M=(8.5,1.5)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=8.5$. Substitute $x_1 = 8$ into the equation: $\frac{8 + x_2}{2}=8.5$. Multiply both sides by 2: $8 + x_2=17$. Then subtract 8 from both sides: $x_2=17 - 8=9$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=1.5$. Substitute $y_1 = 16$ into the equation: $\frac{16 + y_2}{2}=1.5$. Multiply both sides by 2: $16 + y_2 = 3$. Then subtract 16 from both sides: $y_2=3 - 16=-13$.

Answer:

$(9,-13)$