Question

the midpoint m of vw has coordinates (11, 13). point w has coordinates (5, 13). find the coordinates of point v. write the coordinates as decimals or integers.

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 $V$ be $(x,y)$, the coordinates of $W=(5,13)$ and the coordinates of $M=(11,13)$.

Step2: Solve for the x - coordinate of V

We know that $\frac{x + 5}{2}=11$. Multiply both sides by 2: $x + 5=22$. Then subtract 5 from both sides: $x=22 - 5=17$.

Step3: Solve for the y - coordinate of V

We know that $\frac{y + 13}{2}=13$. Multiply both sides by 2: $y+13 = 26$. Then subtract 13 from both sides: $y=26 - 13 = 13$.

Answer:

$(17,13)$