Find an equation for the perpendicular bisector of the line segment whose endpoints are (-5, 1) and (-1, -5).

Given:

The endpoints of a line segment are (-5, 1) and (-1, -5).

To find:

The equation for the perpendicular bisector of the given line segment.

Solution:

The endpoints of a line segment, (-5, 1) and (-1, -5).

perpendicular bisector is perpendicular to the line segment and passes through the midpoint of the line segment.

Midpoint of the given line segment is:

The slope of the segment is:

The product of the slopes of the perpendicular lines is -1.

Slope of perpendicular bisector is and it passes through the point (-3,-2). So, the equation of the perpendicular bisector is

Subtract both sides by 2.

Therefore, the equation of the perpendicular bisector is .

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation: