Question

the midpoint of jk is m(5.5, 8). one endpoint is k(9, 12). 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 $K=(9,12)$ and $M=(5.5,8)$.

Step2: Solve for x - coordinate

We know that $\frac{x + 9}{2}=5.5$. Multiply both sides by 2: $x + 9=11$. Then subtract 9 from both sides: $x=11 - 9=2$.

Step3: Solve for y - coordinate

We know that $\frac{y + 12}{2}=8$. Multiply both sides by 2: $y + 12=16$. Then subtract 12 from both sides: $y=16 - 12 = 4$.

Answer:

$(2,4)$