Translate (2, 3) by (x, y) -> (x - 4, y + 1)

Step by step

The question

Question: translate the point P(2, 3) by the rule: (x, y) goes to (x − 4, y + 1).

1 Draw the shape

Put the point on the grid.

2 Read the move

Left 4 means x gets 4 smaller: x − 4.

Up 1 means y gets 1 bigger: y + 1.

So the move is: left 4, up 1.

3 Move each point

Start at P.

Go left 4.

Then go up 1.

We land on the new point.

We call the new point P prime.

The little mark means: the new P.

P is (2, 3).

Left 4: 2 minus 4 is −2.

Up 1: 3 plus 1 is 4.

So P' is (−2, 4).

Careful!

Left makes x smaller.

So we take 4 away.

We do not add it.

4 The new point

So the image is P'(−2, 4).

5 Check

Let's check.

Draw an arrow from each point to its new point.

The arrow goes left 4, up 1.

Right!

Let's look back.

First: draw the shape.

Then: read the move.

Then: move each point.

Then: the new point.

Last: check.