Question

the midpoint of jk is m(24.5, 55). one endpoint is k(-80, 52). find the coordinates of the other endpoint j. write the coordinates as decimals or integers. j=( , )

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 $J=(x,y)$ and $K=(-80,52)$ and $M=(24.5,55)$.

Step2: Solve for the x - coordinate of J

We have $\frac{x+( - 80)}{2}=24.5$. Multiply both sides by 2: $x - 80=24.5\times2=49$. Then add 80 to both sides: $x=49 + 80=129$.

Step3: Solve for the y - coordinate of J

We have $\frac{y + 52}{2}=55$. Multiply both sides by 2: $y+52 = 110$. Then subtract 52 from both sides: $y=110 - 52 = 58$.

Answer:

$(129,58)$