Question

kl has a mid - point at m(0, 1). point k is at (10, 2). find the coordinates of point l. l=( , ) as decimals or integers.

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 $K=(x_1,y_1)=(10,2)$ and $L=(x_2,y_2)$, and $M=(0,1)$.

Step2: Solve for $x$ - coordinate of $L$

We know that $\frac{x_1 + x_2}{2}=0$. Substitute $x_1 = 10$ into the equation: $\frac{10+x_2}{2}=0$. Multiply both sides by 2: $10 + x_2=0$. Then $x_2=- 10$.

Step3: Solve for $y$ - coordinate of $L$

We know that $\frac{y_1 + y_2}{2}=1$. Substitute $y_1 = 2$ into the equation: $\frac{2+y_2}{2}=1$. Multiply both sides by 2: $2 + y_2=2$. Then $y_2=0$.

Answer:

$(-10,0)$