Question

the mid - point m of uv has coordinates (4, 4). point u has coordinates (5, 0). 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 $U=(x_1,y_1)=(5,0)$ and $M=(x_m,y_m)=(4,4)$, and $V=(x_2,y_2)$.

Step2: Solve for $x$ - coordinate of $V$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, $4=\frac{5 + x_2}{2}$. Cross - multiply: $4\times2=5 + x_2$. So, $8 = 5+x_2$. Then $x_2=8 - 5=3$.

Step3: Solve for $y$ - coordinate of $V$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the values, $4=\frac{0 + y_2}{2}$. Cross - multiply: $4\times2=0 + y_2$. So, $y_2 = 8$.

Answer:

$(3,8)$