Question

the midpoint m of jk has coordinates (9, 7.5). point k has coordinates (15, 1). 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 of point $K$ be $(15,1)$ and mid - point $M$ be $(9,7.5)$.

Step2: Solve for $x$ - coordinate of $J$

We know that $\frac{x + 15}{2}=9$. Multiply both sides by 2: $x + 15=18$. Then subtract 15 from both sides: $x=18 - 15=3$.

Step3: Solve for $y$ - coordinate of $J$

We know that $\frac{y + 1}{2}=7.5$. Multiply both sides by 2: $y + 1 = 15$. Then subtract 1 from both sides: $y=15 - 1=14$.

Answer:

$(3,14)$