Question

vw has a midpoint at m(20.5, 43). point w is at (13, 15). 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 the coordinates of point $V$ be $(x,y)$ and point $W=(13,15)$ and mid - point $M=(20.5,43)$.

Step2: Solve for $x$

We know that $\frac{x + 13}{2}=20.5$. Multiply both sides by 2: $x + 13=20.5\times2=41$. Then subtract 13 from both sides: $x=41 - 13=28$.

Step3: Solve for $y$

We know that $\frac{y + 15}{2}=43$. Multiply both sides by 2: $y + 15=43\times2 = 86$. Then subtract 15 from both sides: $y=86-15 = 71$.

Answer:

$(28,71)$