Question

the midpoint n of uv has coordinates (8, 2). point v has coordinates (6, 2). 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 $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the coordinates of point $U$ be $(x,y)$ and the mid - point $N(8,2)$ and point $V(6,2)$.

Step2: Find the x - coordinate of point U

For the x - coordinate, we have $\frac{x + 6}{2}=8$. Multiply both sides by 2: $x + 6=16$. Then subtract 6 from both sides: $x=16 - 6=10$.

Step3: Find the y - coordinate of point U

For the y - coordinate, we have $\frac{y + 2}{2}=2$. Multiply both sides by 2: $y+2 = 4$. Then subtract 2 from both sides: $y=4 - 2=2$.

Answer:

$(10,2)$