# How do I find the equation of a perpendicular bisector of a line segment with the endpoints #(-2, -4)# and #(6, 4)#?

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Here's how.

You need to find the slope of the segment since it is the **negative reciprocal** of the slope of the bisector.

Another one you will have to find is the **midpoint** of the segment because the bisector will pass trough that point.

If you have those two, you can now determine the equation of the perpendicular bisector using **point-slope form** of a line.

Let:

**Solving for the slope of the segment:**

**Solving for the slope of the bisector:**

**Solving for the midpoint of the segment:**

**Solving for the equation of the segment:**

**POINT-SLOPE FORM**

**slope-intercept form**

**standard form**

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Let

This can be rewritten as

Using

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