Question

one endpoint of a line segment is located at $(1,-5)$. the other endpoint is 10 units left and the y - coordinate of the midpoint of the segment is 2. 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 \(x_1 = 1\). The other endpoint is \(10\) units left of the first, so \(x_2=1 - 10=-9\).

Step2: Use the mid - point formula for the \(y\)-coordinate

The mid - point formula for the \(y\)-coordinate is \(y_m=\frac{y_1 + y_2}{2}\). We know \(y_m = 2\) and \(y_1=-5\).
Substitute into the formula: \(2=\frac{-5 + y_2}{2}\).
Multiply both sides by \(2\): \(4=-5 + y_2\).
Add \(5\) to both sides: \(y_2=4 + 5=9\).

So the ordered pair of the other endpoint is \((-9,9)\).

Answer:

\((-9,9)\)