Glide reflect (2, 3): translate 3 left, then reflect in the x-axis Step by Step

Step by step

The question

Question: glide reflect the point P(2, 3): translate left 3, then reflect in the x-axis.

P = (2, 3)

= slide left 3, flip in 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.

glide reflection = slide along the mirror line + flip

Careful!

The mirror line is flat.

So the slide goes left or right, along it.

Any other slide is not a glide.

Careful: the slide goes along the mirror line: left or right

2 Slide

Left 3: x gets 3 smaller.

The rule: (x − 3, y).

slide left 3: (x, y) → (x − 3, y)

P is (2, 3): it goes to (−1, 3).

P(2, 3) → P'(−1, 3)

3 Flip

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

The rule: (x, −y).

flip in x-axis: (x, y) → (x, −y)

P' is (−1, 3): it goes to (−1, −3).

P'(−1, 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(2, 3) → (2, −3) → (−1, −3)

Let's look back.

First: draw the shape.

Then: slide.

Then: flip.

Last: check.

Answer