Question

one endpoint of a line segment is located at (20,5). the other endpoint is 40 units left and the y - coordinate of the midpoint of the segment is 4. write the ordered pair that represents the other end of the segment.

Explanation:

Step1: Find the x - coordinate of the other endpoint

One endpoint has \(x\) - coordinate \(x_1 = 20\). The other endpoint is \(40\) units left of the first one. Using the formula for the \(x\) - coordinate of a point in a line segment (if we consider the movement along the \(x\) - axis), \(x_2=x_1 - 40\). Substituting \(x_1 = 20\), we get \(x_2=20 - 40=-20\).

Step2: Find the y - coordinate of the other endpoint

The mid - point formula for the \(y\) - coordinate is \(y_m=\frac{y_1 + y_2}{2}\). We know \(y_m = 4\) and \(y_1 = 5\). Substituting into the formula \(4=\frac{5 + y_2}{2}\).
Multiply both sides by \(2\): \(8=5 + y_2\).
Subtract \(5\) from both sides: \(y_2=8 - 5 = 3\).

So the ordered pair representing the other end of the segment is \((-20,3)\).

Answer:

\((-20,3)\)