The given line segment has a midpoint at (3, 1). On a coordinate plane, a line goes through (2, 4), (3, 1), and (4, negative 2).

What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?

y = One-thirdx
y = One-thirdx – 2
y = 3x
y = 3x − 8

Step-by-step explanation:

The given line segment has a midpoint at (3, 1) and goes through (2, 4), (3, 1), and (4, -2). We can use any two of the three points to calculate the equation of the line. Let us use the points (2, 4) and (4, -2)

Therefore the line goes through (2, 4) and (4, -2). The equation of a line passing through is:

.

Therefore the line passing through (2, 4) and (4, -2) has an equation:

Comparing with the general equation of line: y = mx + c, the slope (m) = -3 and the intercept on the y axis (c) = 10

Two lines are said to be perpendicular if the product of their slope is -1. If the slope of line one is m1 and the slope of line 2 = m2, then the two lines are perpendicular if:

.

Therefore The slope (m2) of the perpendicular bisector of y = -3x + 10 is:

Since it is the  perpendicular bisector of the given line segment, it passes through the midpoint (3, 1). The equation of the perpendicular bisector is:

the equation, in slope-intercept form, of the perpendicular bisector of the given line segment is