Question

the midpoint m of $overline{uv}$ has coordinates (4, 3). point u has coordinates (1, 3). 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 $U=(x_1,y_1)=(1,3)$ and $V=(x_2,y_2)$, and $M=(4,3)$.

Step2: Find the x - coordinate of V

We know that $\frac{x_1 + x_2}{2}=4$. Substitute $x_1 = 1$ into the equation: $\frac{1+x_2}{2}=4$. Multiply both sides by 2: $1 + x_2=8$. Then subtract 1 from both sides: $x_2=7$.

Step3: Find the y - coordinate of V

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

Answer:

$(7,3)$