Question

jk has a mid - point at m(-10, 8). point j is at (-10, -16). 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 $J(x_1,y_1)=(-10,-16)$ and $K(x_2,y_2)$ and $M(x_m,y_m)=(-10,8)$.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting $x_m=-10$ and $x_1=-10$ into the formula:
\[

$$\begin{align*} -10&=\frac{-10 + x_2}{2}\\ -10\times2&=-10 + x_2\\ -20&=-10 + x_2\\ x_2&=-20 + 10=-10 \end{align*}$$

\]

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting $y_m = 8$ and $y_1=-16$ into the formula:
\[

$$\begin{align*} 8&=\frac{-16 + y_2}{2}\\ 8\times2&=-16 + y_2\\ 16&=-16 + y_2\\ y_2&=16 + 16 = 32 \end{align*}$$

\]

Answer:

$K=(-10,32)$