Question

kl has a midpoint at m(15.5, 7.5). point l is at (16, 11). find the coordinates of point 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 the coordinates of point $K$ be $(x,y)$ and point $L(16,11)$ and mid - point $M(15.5,7.5)$.

Step2: Solve for x - coordinate of K

We know that $\frac{x + 16}{2}=15.5$. Multiply both sides by 2: $x + 16=15.5\times2 = 31$. Then subtract 16 from both sides: $x=31 - 16=15$.

Step3: Solve for y - coordinate of K

We know that $\frac{y + 11}{2}=7.5$. Multiply both sides by 2: $y + 11=7.5\times2 = 15$. Then subtract 11 from both sides: $y=15 - 11 = 4$.

Answer:

$(15,4)$