Question

Which of the following represents an equation of the line that is the perpendicular bisector of the segment whose endpoints are (-2, 4) and (8, 4)?

A) x = 3
B) y = 3
C) x = 5
D) y = 5

Answer 1

The perpendicular bisector of the segment with endpoints (-2, 4) and (8, 4) is a vertical line passing through their midpoint. The midpoint is (3, 4), therefore the equation of the perpendicular bisector is A) x = 3.

Step-by-step explanation:

To identify the equation of the line that is the perpendicular bisector of the line segment with endpoints (-2, 4) and (8, 4), we need to find the midpoint of the segment and the slope that is perpendicular to the slope of the original segment.

Firstly, the midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is given by ((x1 + x2)/2, (y1 + y2)/2). Applying this formula to our endpoints gives us M = ((-2 + 8)/2, (4 + 4)/2) = (3, 4).

Secondly, the original line segment has a slope of 0, because the y-coordinates are the same and the slope formula (delta y / delta x) would yield 0. A perpendicular slope to a horizontal line is undefined, which means the perpendicular bisector is a vertical line.

Since the midpoint's x-coordinate is 3, the equation of our perpendicular bisector is a vertical line crossing the x-axis at x = 3. Therefore, the correct answer is A) x = 3.