Question

uv has a midpoint at m(6, 3). point u is at (3, 9). 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 $U(x_1,y_1)=(3,9)$ and $V(x_2,y_2)$. The mid - point $M(6,3)$.

Step2: Find the x - coordinate of V

We know that $\frac{x_1 + x_2}{2}=6$. Substitute $x_1 = 3$ into the equation: $\frac{3+x_2}{2}=6$. Multiply both sides by 2: $3 + x_2=12$. Then subtract 3 from both sides: $x_2=12 - 3=9$.

Step3: Find the y - coordinate of V

We know that $\frac{y_1 + y_2}{2}=3$. Substitute $y_1 = 9$ into the equation: $\frac{9+y_2}{2}=3$. Multiply both sides by 2: $9 + y_2=6$. Then subtract 9 from both sides: $y_2=6 - 9=-3$.

Answer:

$(9,-3)$