Question

the midpoint of $overline{kl}$ is $m(1,9)$. one endpoint is $k(2,9)$. find the coordinates of the other endpoint $l$. write the coordinates as decimals or integers. $l = (square square)$

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 $K(2,9)=(x_1,y_1)$ and $L=(x_2,y_2)$, and $M(1,9)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=1$. Substitute $x_1 = 2$ into the equation: $\frac{2+x_2}{2}=1$. Multiply both sides by 2: $2 + x_2=2$. Then subtract 2 from both sides: $x_2=0$.

Step3: Solve for $y_2$

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: $y_2=9$.

Answer:

$(0,9)$