Question

the midpoint m of (overline{jk}) has coordinates ((5,5)). point k has coordinates ((10,6)). 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 the coordinates of point $K$ be $(10,6)$ and the mid - point $M$ be $(5,5)$.

Step2: Solve for $x$

We know that $\frac{x + 10}{2}=5$. Multiply both sides by 2: $x + 10=10$. Then subtract 10 from both sides: $x=0$.

Step3: Solve for $y$

We know that $\frac{y + 6}{2}=5$. Multiply both sides by 2: $y+6 = 10$. Then subtract 6 from both sides: $y = 4$.

Answer:

$(0,4)$