Question

the midpoint m of jk has coordinates (-1, 9). point j has coordinates (-8, 9). 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 $J(x_1,y_1)=(-8,9)$ and $K(x_2,y_2)$ and $M(-1,9)$.

Step2: Solve for the x - coordinate of K

We know that $\frac{x_1 + x_2}{2}=-1$. Substitute $x_1=-8$ into the equation: $\frac{-8 + x_2}{2}=-1$. Multiply both sides by 2: $-8 + x_2=-2$. Then add 8 to both sides: $x_2=-2 + 8=6$.

Step3: Solve for the y - coordinate of K

We know that $\frac{y_1 + y_2}{2}=9$. Substitute $y_1 = 9$ into the equation: $\frac{9 + y_2}{2}=9$. Multiply both sides by 2: $9 + y_2=18$. Subtract 9 from both sides: $y_2=18 - 9=9$.

Answer:

$(6,9)$