Question

the midpoint m of (overline{jk}) has coordinates (9, 7.5). point j has coordinates (-2, -5). find the coordinates of point k. write the coordinates as decimals or integers. k = ( , )

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 $J(x_1,y_1)=(-2,-5)$ and $K(x_2,y_2)$. The mid - point $M=(9,7.5)$.

Step2: Solve for the x - coordinate of K

We know that $\frac{x_1 + x_2}{2}=9$. Substitute $x_1=-2$ into the equation: $\frac{-2 + x_2}{2}=9$. Multiply both sides by 2: $-2+x_2 = 18$. Then add 2 to both sides: $x_2=18 + 2=20$.

Step3: Solve for the y - coordinate of K

We know that $\frac{y_1 + y_2}{2}=7.5$. Substitute $y_1=-5$ into the equation: $\frac{-5 + y_2}{2}=7.5$. Multiply both sides by 2: $-5+y_2=15$. Then add 5 to both sides: $y_2=15 + 5=20$.

Answer:

$(20,20)$