Write the equation of the perpendicular bisector of ab

As the name suggests, the perpendicular bisector of a given segment is a line that  is perpendicular to the given one and passes through its midpoint.

Remember that, if a line has slope m, a perpendicular line will have slope k, such that mk = -1.

Step 1: Slope of AB

We compute the slope with the usual formula

Step 2: Perpendicular Slope

We're looking for a slope k such that

Step 3: Midpoint of AB

The coordinates of the midpoint are the average of the coordinates of the endpoint. So, the midpoint M has coordinates

So, the midpoint is (5/2,9/2)

Step 4: line equation

If you know the slope of a line, and a point belonging to it, the equation of the line is given by

Plug your values:

Which you can rearrange as

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step-by-step explanation:

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