Question

the midpoint of $overline{kl}$ is $m(11.5, 11.5)$. one endpoint is $k(11, 16)$. 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 $K(x_1,y_1)=(11,16)$ and $L(x_2,y_2)$. We know $M(11.5,11.5)$.

Step2: Find the x - coordinate of L

Set up the equation for the x - coordinate of the mid - point: $\frac{x_1+x_2}{2}=11.5$. Substitute $x_1 = 11$ into the equation: $\frac{11+x_2}{2}=11.5$. Multiply both sides by 2: $11+x_2=23$. Then solve for $x_2$: $x_2=23 - 11=12$.

Step3: Find the y - coordinate of L

Set up the equation for the y - coordinate of the mid - point: $\frac{y_1+y_2}{2}=11.5$. Substitute $y_1 = 16$ into the equation: $\frac{16+y_2}{2}=11.5$. Multiply both sides by 2: $16+y_2=23$. Then solve for $y_2$: $y_2=23 - 16 = 7$.

Answer:

$(12,7)$