Question

the midpoint m of jk has coordinates (-13, 13). point k has coordinates (-16, 20), 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 $(x,y)$ and point $K(-16,20)$ and mid - point $M(-13,13)$.

Step2: Solve for the x - coordinate of J

We know that $\frac{x+( - 16)}{2}=-13$. Multiply both sides by 2: $x - 16=-26$. Then add 16 to both sides: $x=-26 + 16=-10$.

Step3: Solve for the y - coordinate of J

We know that $\frac{y + 20}{2}=13$. Multiply both sides by 2: $y+20 = 26$. Then subtract 20 from both sides: $y=26 - 20 = 6$.

Answer:

$(-10,6)$