Question

Write an equation of the perpendicular bisector of the segment with the endpoints.

a) x - (x1 + x2)/2 = 0
b) y - (y1 + y2)/2 = 0
c) y - (y1 + y2)/2 = -(x2 - x1)/(y2 - y1) * (x - (x1 + x2)/2)
d) y - (y1 + y2)/2 = (x2 - x1)/(y2 - y1) * (x - (x1 + x2)/2)

Answer 1

The correct equation of the perpendicular bisector is option d) y - (y1 + y2)/2 = (x2 - x1)/(y2 - y1) * (x - (x1 + x2)/2).

Step-by-step explanation:

The correct equation of the perpendicular bisector of a segment with the endpoints (x1, y1) and (x2, y2) is option d) y - (y1 + y2)/2 = (x2 - x1)/(y2 - y1) * (x - (x1 + x2)/2). This equation represents a line that passes through the midpoint of the segment and is perpendicular to it. The equation is derived using the midpoint formula and the negative reciprocal of the slope of the segment.