Perpendicular bisector of (3, -2) and (3, 6) Step by Step

Step by step

The question

Question: find the perpendicular bisector of A(3, −2) and B(3, 6).

perpendicular bisector of A(3, −2) and B(3, 6)

The perpendicular bisector cuts A B in half, at a right angle.

So it goes through the middle of A B.

bisector = cuts AB in half

perpendicular = at 90° to AB

1 Find the midpoint

The midpoint is the average of the x's and the average of the y's: (3, 2).

M = (3 + 32, −2 + 62) = (3, 2)

2 Slope of AB

A and B have the same x: A B is a vertical line.

slope of AB = undefined: AB goes straight up

3 Perpendicular slope

At 90° to a vertical line is a flat line.

perpendicular line = flat

4 Write the equation

A flat line through M: every point has y = 2.

So y = 2.

= y = 2

5 Draw it

Let's draw it on the grid.

A and B, and the segment between them.

M in the middle.

The bisector goes through M, across A B.

It meets A B at a right angle.

6 Check

Let's check with another point on the line, (5, 2).

Its distance squared to A and to B is the same: 20.

Every point on the bisector is as far from A as from B.

So it is right!

point (5, 2) on the line: to A² = 20, to B² = 20

Let's look back.

First: find the midpoint.

Then: slope of AB.

Then: perpendicular slope.

Then: write the equation.

Then: draw it.

Last: check.

Answer