Translate A(2, 2) B(5, 3) C(3, 5) by (x, y) -> (x - 6, y

Step by step

The question

Question: translate the shape A(2, 2), B(5, 3) and C(3, 5) by the rule: (x, y) goes to (x − 6, y − 4).

A(2, 2), B(5, 3) and C(3, 5)

= (x, y) → (x − 6, y − 4)

1 Draw the shape

Put the points on the grid and join them.

2 Read the move

Left 6 means x gets 6 smaller: x − 6.

x − 6 → left 6

Down 4 means y gets 4 smaller: y − 4.

y − 4 → down 4

So the move is: left 6, down 4.

3 Move each point

Start at A.

Go left 6.

Then go down 4.

We land on the new point.

We call the new point A prime.

The little mark means: the new A.

A is (2, 2).

Left 6: 2 minus 6 is −4.

Down 4: 2 minus 4 is −2.

So A' is (−4, −2).

A(2, 2) → (2 − 6, 2 − 4) = A'(−4, −2)

Careful!

Down makes y smaller.

So we take 4 away.

We do not add it.

Careful: not A'(2 − 6, 2 + 4) ✗

Now B: 5 minus 6 is −1.

3 minus 4 is −1.

So B' is (−1, −1).

B(5, 3) → (5 − 6, 3 − 4) = B'(−1, −1)

Now C: 3 minus 6 is −3.

5 minus 4 is 1.

So C' is (−3, 1).

C(3, 5) → (3 − 6, 5 − 4) = C'(−3, 1)

4 Draw the image

Join the new points.

This new shape is called the image.

So the image is A'(−4, −2), B'(−1, −1) and C'(−3, 1).

A'(−4, −2), B'(−1, −1) and C'(−3, 1)

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 6, down 4

Let's look back.

First: draw the shape.

Then: read the move.

Then: move each point.

Then: draw the image.

Last: check.

Answer