Question

one end of a line segment is located at (8, 5) and the midpoint of the segment is located at (-3, 0). write the ordered pair that represents the other end of the segment.

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 $(x_1,y_1)=(8,5)$ and the mid - point $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})=(-3,0)$.

Step2: Solve for $x_2$

We have $\frac{x_1 + x_2}{2}=-3$. Substitute $x_1 = 8$ into the equation: $\frac{8 + x_2}{2}=-3$. Multiply both sides by 2: $8 + x_2=-6$. Then subtract 8 from both sides: $x_2=-6 - 8=-14$.

Step3: Solve for $y_2$

We have $\frac{y_1 + y_2}{2}=0$. Substitute $y_1 = 5$ into the equation: $\frac{5 + y_2}{2}=0$. Multiply both sides by 2: $5 + y_2=0$. Then subtract 5 from both sides: $y_2=-5$.

Answer:

$(-14,-5)$