Question

the midpoint m of $overline{kl}$ has coordinates (-10, -5). point k has coordinates (-8, 0). find the coordinates of point l. write the coordinates as decimals or integers. l = ( )

Explanation:

Step1: Recall mid - point formula

The mid - point formula between 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 $K(x_1,y_1)=(-8,0)$ and $L(x_2,y_2)$, and $M(-10,-5)$.

Step2: Find the x - coordinate of L

We know that $\frac{x_1 + x_2}{2}=-10$. Substitute $x_1=-8$ into the equation: $\frac{-8 + x_2}{2}=-10$. Multiply both sides by 2: $-8 + x_2=-20$. Then add 8 to both sides: $x_2=-20 + 8=-12$.

Step3: Find the y - coordinate of L

We know that $\frac{y_1 + y_2}{2}=-5$. Substitute $y_1 = 0$ into the equation: $\frac{0 + y_2}{2}=-5$. Multiply both sides by 2: $y_2=-10$.

Answer:

$L=(-12,-10)$