The point (5, −1) is translated 3 units left and 4 units up. Write…

Step by step

The question

Question: translate the point P(5, −1) left 3, up 4.

1 Draw the shape

Put the point on the grid.

2 Read the move

In a point (x, y), x tells across and y tells up.

Left 3 means x gets 3 smaller: x − 3.

Up 4 means y gets 4 bigger: y + 4.

So every point (x, y) goes to (x − 3, y + 4).

3 Move each point

Start at P.

Go left 3.

Then go up 4.

We land on the new point.

We call the new point P prime.

The little mark means: the new P.

P is (5, −1).

Left 3: 5 minus 3 is 2.

Up 4: −1 plus 4 is 3.

So P' is (2, 3).

Careful!

Left makes x smaller.

So we take 3 away.

We do not add it.

4 The new point

So the image, the new point, is P'(2, 3).

5 Check

Let's check.

Draw an arrow from each point to its new point.

The arrow goes left 3, up 4.

Right!

Let's look back.

First: draw the shape.

Then: read the move.

Then: move each point.

Then: the new point.

Last: check.