Question

the midpoint m of kl has coordinates (50, 23). point l has coordinates (45, 15). find the coordinates of point k. write the coordinates as decimals or integers.

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 $L=(45,15)$ and mid - point $M=(50,23)$.

Step2: Solve for $x$

We have $\frac{x + 45}{2}=50$. Multiply both sides by 2: $x + 45=100$. Then subtract 45 from both sides: $x=100 - 45=55$.

Step3: Solve for $y$

We have $\frac{y + 15}{2}=23$. Multiply both sides by 2: $y + 15 = 46$. Then subtract 15 from both sides: $y=46-15 = 31$.

Answer:

$(55,31)$