Perpendicular bisector of (2, 1) and (8, 1) Step by Step

Step by step

The question

Question: find the perpendicular bisector of A(2, 1) and B(8, 1).

perpendicular bisector of A(2, 1) and B(8, 1)

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: (5, 1).

M = (2 + 82, 1 + 12) = (5, 1)

2 Slope of AB

A and B have the same y: A B is a flat line.

slope of AB = 0: AB is flat

3 Perpendicular slope

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

perpendicular line = vertical

4 Write the equation

A vertical line through M: every point has x = 5.

So x = 5.

= x = 5

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, 3).

Its distance squared to A and to B is the same: 13.

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

So it is right!

point (5, 3) on the line: to A² = 13, to B² = 13

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