Question

one endpoint of a line segment is located at (10, -5). the other endpoint is 20 units left and the y - coordinate of the midpoint of the segment is 5. write the ordered pair that represents the other end of the segment.

Explanation:

Step1: Find the x - coordinate of the other endpoint

The first endpoint has x - coordinate $x_1 = 10$. The other endpoint is 20 units left, so its x - coordinate $x_2=10 - 20=-10$.

Step2: Use the mid - point formula for the y - coordinate

The mid - point formula for the y - coordinate of a line segment with endpoints $(x_1,y_1)$ and $(x_2,y_2)$ is $y_m=\frac{y_1 + y_2}{2}$, where $y_m = 5$ and $y_1=-5$. We substitute into the formula: $5=\frac{-5 + y_2}{2}$. Multiply both sides by 2: $10=-5 + y_2$. Then add 5 to both sides to solve for $y_2$: $y_2=10 + 5 = 15$.

Answer:

$(-10,15)$