Question

the midpoint m of $overline{uv}$ has coordinates (2, 2). point v has coordinates (3, 1). 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 the coordinates of point $U$ be $(x,y)$ and of point $V$ be $(3,1)$ and mid - point $M$ be $(2,2)$.

Step2: Solve for x - coordinate of U

We have $\frac{x + 3}{2}=2$. Multiply both sides by 2: $x + 3=4$. Then subtract 3 from both sides: $x=4 - 3=1$.

Step3: Solve for y - coordinate of U

We have $\frac{y + 1}{2}=2$. Multiply both sides by 2: $y + 1=4$. Then subtract 1 from both sides: $y=4 - 1=3$.

Answer:

$(1,3)$