# What is the equation of the line that is perpendicular to the line passing through #(-5,12)# and #(4,-3)# at midpoint of the two points?

##### 2 Answers

See a solution process below:

#### Explanation:

First, we need to find the mid-point and of the two points and the slope of the line going through the two points.

The formula to find the mid-point of a line segment give the two end points is:

Where

Substituting the values from the points in the problem gives:

The slope can be found by using the formula:

Where

Substituting the values from the points in the problem gives:

Let's call the slope of a perpendicular line:

The formula for the slope of a perpendicular line is:

Substituting gives:

Now that we have the slope of the perpendicular line and a point on the line (the midpoint of the line segment) we can use the point-slope formula to write an equation for the line. The point-slope form of a linear equation is:

Where

Substituting the slope and the values from the mid-point gives:

#### Explanation:

Given the points:

a. The slope between the given points is

b. The slope of any line perpendicular to this is

c. The midpoint between the given points is

d. The equation, in slope-point form, for the perpendicular through the midpoint is

e. Converting to standard form:

after multiplying both sides by

rearranging into the standard form:

and simplifying by dividing all terms by