Question

the mid - point m of jk has coordinates (16, 5.5). point k has coordinates (20, 4). find the coordinates of point 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 the coordinates of point $J$ be $(x,y)$, point $K=(20,4)$ and mid - point $M=(16,5.5)$.

Step2: Solve for $x$

We know that $\frac{x + 20}{2}=16$. Cross - multiply: $x + 20=32$. Then $x=32−20=12$.

Step3: Solve for $y$

We know that $\frac{y + 4}{2}=5.5$. Cross - multiply: $y + 4 = 11$. Then $y=11−4 = 7$.

Answer:

$(12,7)$