Question

Given are the points A(0,1) and B(4,-7). Find an equation (the point-slope form is perfectly acceptable) of the perpendicular bisector of line segment AB

Answer 1

• y + 3 = 1/2(x - 2)

Explanation:

Find the slope of the given line using the coordinates of A and B.

The slope:

• m = (-7 - 1)/4 = -2

Find the midpoint of segment AB:

• x = (0 + 4)/2 = 2
• y = (1 - 7)/2 = -3

The perpendicular line has a slope of 1/2 ( opposite-reciprocal of -2) and passes through the point (2, -3).

The equation of this line is:

• y - (-3) - 1/2(x - 2)
• y + 3 = 1/2(x - 2)

Slope-intercept form:

• y = 1/2x - 4