Question

kl has a midpoint at m(40, 42). point k is at (68, 12). find the coordinates of point l. write the coordinates as decimals or integers. l = ( )

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 $K(x_1,y_1)=(68,12)$ and $L(x_2,y_2)$, and $M(40,42)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=40$. Substitute $x_1 = 68$ into the equation: $\frac{68+x_2}{2}=40$. Multiply both sides by 2: $68 + x_2=80$. Then subtract 68 from both sides: $x_2=80 - 68=12$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=42$. Substitute $y_1 = 12$ into the equation: $\frac{12+y_2}{2}=42$. Multiply both sides by 2: $12 + y_2=84$. Then subtract 12 from both sides: $y_2=84 - 12 = 72$.

Answer:

$(12,72)$