Translate A(1, 1) B(4, 1) C(1, 3) by (x, y) -> (x

Step by step

The question

Question: translate the shape A(1, 1), B(4, 1) and C(1, 3) by the rule: (x, y) goes to (x − 4, y + 1).

A(1, 1), B(4, 1) and C(1, 3)

= (x, y) → (x − 4, y + 1)

1 Draw the shape

Put the points on the grid and join them.

2 Read the move

Left 4 means x gets 4 smaller: x − 4.

x − 4 → left 4

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

y + 1 → up 1

So the move is: left 4, up 1.

3 Move each point

Start at A.

Go left 4.

Then go up 1.

We land on the new point.

We call the new point A prime.

The little mark means: the new A.

A is (1, 1).

Left 4: 1 minus 4 is −3.

Up 1: 1 plus 1 is 2.

So A' is (−3, 2).

A(1, 1) → (1 − 4, 1 + 1) = A'(−3, 2)

Careful!

Left makes x smaller.

So we take 4 away.

We do not add it.

Careful: not A'(1 + 4, 1 + 1) ✗

Now B: 4 minus 4 is 0.

1 plus 1 is 2.

So B' is (0, 2).

B(4, 1) → (4 − 4, 1 + 1) = B'(0, 2)

Now C: 1 minus 4 is −3.

3 plus 1 is 4.

So C' is (−3, 4).

C(1, 3) → (1 − 4, 3 + 1) = C'(−3, 4)

4 Draw the image

Join the new points.

This new shape is called the image.

So the image is A'(−3, 2), B'(0, 2) and C'(−3, 4).

A'(−3, 2), B'(0, 2) and C'(−3, 4)

5 Check

Let's check.

Draw an arrow from each point to its new point.

All the arrows are the same: the same length, the same way.

So the shape slid, without turning.

Right!

A → A', B → B', C → C': left 4, up 1

Let's look back.

First: draw the shape.

Then: read the move.

Then: move each point.

Then: draw the image.

Last: check.

Answer