Reflect (-4, 1) in the x-axis Step by Step

Step by step

The question

Question: reflect the point P(−4, 1) in the x-axis.

P = (−4, 1)

= in the x-axis

1 Draw the shape

Put the point on the grid.

2 Draw the mirror line

The mirror line is the x-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: 1.

Then count 1 more on the other side.

We call the new point P prime.

The little mark means: the new P.

P is 1 above the x-axis.

Its image is 1 below it.

Its x stays −4.

So P' is (−4, −1).

P(−4, 1) → P'(−4, −1)

Careful!

The x-axis is flat.

The flip goes up or down, so y changes.

x stays.

Careful: not P'(4, 1) ✗

4 The new point

So the image is P'(−4, −1).

P' = (−4, −1)

5 Check

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

x-axis: (x, y) → (x, −y)

It gives the same points.

Right!

P(−4, 1) → P'(−4, −1)

Let's look back.

First: draw the shape.

Then: draw the mirror line.

Then: reflect each point.

Then: the new point.

Last: check.

Answer