Question

kl has a mid - point at m(14.5, 12.5). point l is at (18, 5). find the coordinates of point k. write the coordinates as decimals or integers. k = ( , )

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $K(x_1,y_1)$ and $L(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. We know $M(14.5,12.5)$ and $L(18,5)$.

Step2: Solve for the x - coordinate of K

Let the coordinates of $K$ be $(x,y)$. Using the x - coordinate part of the mid - point formula $\frac{x + 18}{2}=14.5$. Multiply both sides by 2: $x + 18=29$. Then subtract 18 from both sides: $x=29 - 18=11$.

Step3: Solve for the y - coordinate of K

Using the y - coordinate part of the mid - point formula $\frac{y + 5}{2}=12.5$. Multiply both sides by 2: $y + 5 = 25$. Then subtract 5 from both sides: $y=25 - 5=20$.

Answer:

$(11,20)$