Question

the midpoint of $overline{jk}$ is $m(-6.5, -7.5)$. one endpoint is $j(-8, -12)$. find the coordinates of the other endpoint $k$. 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 $J(x_1,y_1)=(-8,-12)$ and $K(x_2,y_2)$. The mid - point $M(-6.5,-7.5)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-6.5$. Substitute $x_1=-8$ into the equation: $\frac{-8 + x_2}{2}=-6.5$. Multiply both sides by 2: $-8 + x_2=-13$. Then add 8 to both sides: $x_2=-13 + 8=-5$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=-7.5$. Substitute $y_1=-12$ into the equation: $\frac{-12 + y_2}{2}=-7.5$. Multiply both sides by 2: $-12 + y_2=-15$. Then add 12 to both sides: $y_2=-15 + 12=-3$.

Answer:

$(-5,-3)$