Reflect (3, 2) in the y-axis Step by Step

Step by step

The question

Question: reflect the point P(3, 2) in the y-axis.

P = (3, 2)

= in the y-axis

1 Draw the shape

Put the point on the grid.

2 Draw the mirror line

The mirror line is the y-axis.

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

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

reflection = flip

3 Reflect each point

From P, count straight to the mirror line: 3.

Then count 3 more on the other side.

We call the new point P prime.

The little mark means: the new P.

P is 3 right of the y-axis.

Its image is 3 left of it.

Its y stays 2.

So P' is (−3, 2).

P(3, 2) → P'(−3, 2)

Careful!

The y-axis goes up and down.

The flip goes left or right, so x changes.

y stays.

Careful: not P'(3, −2) ✗

4 The new point

So the image is P'(−3, 2).

P' = (−3, 2)

5 Check

Let's check with the rule for the y-axis: x changes sign, y stays the same.

y-axis: (x, y) → (−x, y)

It gives the same points.

Right!

P(3, 2) → P'(−3, 2)

Let's look back.

First: draw the shape.

Then: draw the mirror line.

Then: reflect each point.

Then: the new point.

Last: check.

Answer