Question

given the endpoint (5,0) and midpoint (-3,3). find the other endpoint. answer attempt 1 out of 2

Explanation:

Step1: Recall mid - point formula

The mid - point formula between 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 $(x_1,y_1)=(5,0)$ and the mid - point $(x_m,y_m)=(-3,3)$.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, we have $-3=\frac{5 + x_2}{2}$. Cross - multiply: $-3\times2=5 + x_2$, so $-6 = 5+x_2$. Then $x_2=-6 - 5=-11$.

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the values, we have $3=\frac{0 + y_2}{2}$. Cross - multiply: $3\times2=0 + y_2$, so $y_2 = 6$.

Answer:

$(-11,6)$