Glide reflect (3, 1): translate 4 down, then reflect in the line x = 2 Step by Step

Step by step

The question

Question: glide reflect the point P(3, 1): translate down 4, then reflect in the line x = 2.

P = (3, 1)

= slide down 4, flip in line x = 2

1 Draw the shape

Put the point on the grid.

The mirror line is the line x = 2.

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

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

glide reflection = slide along the mirror line + flip

Careful!

The mirror line is upright.

So the slide goes up or down, along it.

Any other slide is not a glide.

Careful: the slide goes along the mirror line: up or down

2 Slide

Down 4: y gets 4 smaller.

The rule: (x, y − 4).

slide down 4: (x, y) → (x, y − 4)

P is (3, 1): it goes to (3, −3).

P(3, 1) → P'(3, −3)

3 Flip

Flip in the line x = 2: count from the point to the line, then the same again on the other side.

flip in line x = 2: count to the line, the same again

P' is (3, −3): it goes to (1, −3).

P'(3, −3) → P''(1, −3)

So the image is P''(1, −3).

P'' = (1, −3)

4 Check

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

For a glide, it must give the same points.

flip first, then slide:

The same points as before.

Right!

P(3, 1) → (1, 1) → (1, −3)

Let's look back.

First: draw the shape.

Then: slide.

Then: flip.

Last: check.

Answer