Translate A(0, 0) B(3, 0) C(0, 2) by (x, y) -> (x + 2, y

Step by step

The question

Question: translate the shape A(0, 0), B(3, 0) and C(0, 2) by the rule: (x, y) goes to (x + 2, y − 5).

A(0, 0), B(3, 0) and C(0, 2)

= (x, y) → (x + 2, y − 5)

1 Draw the shape

Put the points on the grid and join them.

2 Read the move

Right 2 means x gets 2 bigger: x + 2.

x + 2 → right 2

Down 5 means y gets 5 smaller: y − 5.

y − 5 → down 5

So the move is: right 2, down 5.

3 Move each point

Start at A.

Go right 2.

Then go down 5.

We land on the new point.

We call the new point A prime.

The little mark means: the new A.

A is (0, 0).

Right 2: 0 plus 2 is 2.

Down 5: 0 minus 5 is −5.

So A' is (2, −5).

A(0, 0) → (0 + 2, 0 − 5) = A'(2, −5)

Careful!

Down makes y smaller.

So we take 5 away.

We do not add it.

Careful: not A'(0 + 2, 0 + 5) ✗

Now B: 3 plus 2 is 5.

0 minus 5 is −5.

So B' is (5, −5).

B(3, 0) → (3 + 2, 0 − 5) = B'(5, −5)

Now C: 0 plus 2 is 2.

2 minus 5 is −3.

So C' is (2, −3).

C(0, 2) → (0 + 2, 2 − 5) = C'(2, −3)

4 Draw the image

Join the new points.

This new shape is called the image.

So the image is A'(2, −5), B'(5, −5) and C'(2, −3).

A'(2, −5), B'(5, −5) and C'(2, −3)

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': right 2, down 5

Let's look back.

First: draw the shape.

Then: read the move.

Then: move each point.

Then: draw the image.

Last: check.

Answer