Glide reflect (4, 2): translate 2 right, then reflect in the x-axis

Step by step

The question

Question: glide reflect the point P(4, 2): translate right 2, then reflect in the x-axis.

1 Draw the shape

Put the point on the grid.

The mirror line is the x-axis.

A glide reflection is a slide along the mirror line, and a flip in it.

Like footprints in the sand: left, right, left.

Careful!

The mirror line is flat.

So the slide goes left or right, along it.

Any other slide is not a glide.

2 Slide

Right 2: x gets 2 bigger.

The rule: (x + 2, y).

P is (4, 2): it goes to (6, 2).

3 Flip

Flip in the x-axis: y changes sign, x stays.

The rule: (x, −y).

P' is (6, 2): it goes to (6, −2).

So the image is P''(6, −2).

4 Check

Let's check the other way round: flip first, then slide.

For a glide, it must give the same points.

The same points as before.

Right!

Let's look back.

First: draw the shape.

Then: slide.

Then: flip.

Last: check.