# What is the equation of the line that is perpendicular to the line passing through #(5,12)# and #(6,14)# at midpoint of the two points?

##### 1 Answer

In point-slope form:

#### Explanation:

First, we need to find the slope of the original line from the two points.

Plugging in corresponding values yields:

Since the slopes of perpendicular lines are negative reciprocals of each other, the slope of the lines we’re looking for is going to be the reciprocal of

Now we need to find the midpoint of those two points, which will give us the remaining information to write the equation of the line.

The midpoint formula is:

Plugging in yields:

Therefore, the line we’re trying to find teh equation of passes through that point.

Knowing the slope of the line, as well as a point where it passes through, we can write its equation in point-slope form, denoted by:

Plugging in yields: