Question

given the endpoint (5,10) and the midpoint (-5,8), find the other endpoint. answer attempt 1 out of 3

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $(x_1,y_1)=(5,10)$ and the mid - point $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})=(-5,8)$.

Step2: Solve for $x_2$

We have $\frac{x_1 + x_2}{2}=-5$. Substitute $x_1 = 5$ into the equation: $\frac{5 + x_2}{2}=-5$. Multiply both sides by 2: $5+x_2=-10$. Then subtract 5 from both sides: $x_2=-10 - 5=-15$.

Step3: Solve for $y_2$

We have $\frac{y_1 + y_2}{2}=8$. Substitute $y_1 = 10$ into the equation: $\frac{10 + y_2}{2}=8$. Multiply both sides by 2: $10 + y_2=16$. Then subtract 10 from both sides: $y_2=16 - 10 = 6$.

Answer:

$(-15,6)$