# Given point A #(-2,1)# and point B #(1,3)#, how do you find the equation of the line perpendicular to the line AB at its midpoint?

##### 1 Answer

Find the midpoint and slope of the Line AB and make the slope a negative reciprocal then to find the y axis plug in the midpoint coordinate. Your answer will be

#### Explanation:

If point A is (-2, 1) and point B is (1, 3) and you need to find the line perpendicular to that line and passes through the midpoint you first need to find the midpoint of AB. To do this you plug it into the equation

So for our midpoint of AB we get (-.5, 2). Now we need to find the slope of AB. to do this we use

So our slope of line AB is 3/2. Now we take the **opposite reciprocal*** of the slope to make a new line equation. Which is

So put b back in the get

***opposite reciprocal** is a fraction with the top and bottom numbers switched then multiplied by -1