Reflect (2, 3) in the line x = 4

Step by step

The question

Question: reflect the point P(2, 3) in the line x = 4.

1 Draw the shape

Put the point on the grid.

2 Draw the mirror line

The mirror line is the line x = 4.

Reflecting flips the shape over the line, like a mirror.

Each point lands just as far away, on the other side.

3 Reflect each point

From P, count straight to the mirror line: 2.

Then count 2 more on the other side.

We call the new point P prime.

The little mark means: the new P.

P is 2 left of the line.

Its image is 2 right of it.

Its y stays 3.

So P' is (6, 3).

Careful!

Count to the mirror line x = 4, not to the y-axis.

4 The new point

So the image is P'(6, 3).

5 Check

Let's check: the mirror line is halfway between a point and its image.

Halfway between 2 and 6: add them, then divide by 2.

That is 4: the line x = 4.

Right!

Let's look back.

First: draw the shape.

Then: draw the mirror line.

Then: reflect each point.

Then: the new point.

Last: check.