Translate A(-4, -1) B(-1, -1) C(-1, 2) D(-4, 2) by (x, y) -> (x + 5… Step by Step

Step by step

The question

Question: translate the shape A(−4, −1), B(−1, −1), C(−1, 2) and D(−4, 2) by the rule: (x, y) goes to (x + 5, y − 2).

A(−4, −1), B(−1, −1), C(−1, 2) and D(−4, 2)

= (x, y) → (x + 5, y − 2)

1 Draw the shape

Put the points on the grid and join them.

2 Read the move

Right 5 means x gets 5 bigger: x + 5.

x + 5 → right 5

Down 2 means y gets 2 smaller: y − 2.

y − 2 → down 2

So the move is: right 5, down 2.

3 Move each point

Start at A.

Go right 5.

Then go down 2.

We land on the new point.

We call the new point A prime.

The little mark means: the new A.

A is (−4, −1).

Right 5: −4 plus 5 is 1.

Down 2: −1 minus 2 is −3.

So A' is (1, −3).

A(−4, −1) → (−4 + 5, −1 − 2) = A'(1, −3)

Careful!

Down makes y smaller.

So we take 2 away.

We do not add it.

Careful: not A'(−4 + 5, −1 + 2) ✗

Now B: −1 plus 5 is 4.

−1 minus 2 is −3.

So B' is (4, −3).

B(−1, −1) → (−1 + 5, −1 − 2) = B'(4, −3)

Now C: −1 plus 5 is 4.

2 minus 2 is 0.

So C' is (4, 0).

C(−1, 2) → (−1 + 5, 2 − 2) = C'(4, 0)

Now D: −4 plus 5 is 1.

2 minus 2 is 0.

So D' is (1, 0).

D(−4, 2) → (−4 + 5, 2 − 2) = D'(1, 0)

4 Draw the image

Join the new points.

This new shape is called the image.

So the image is A'(1, −3), B'(4, −3), C'(4, 0) and D'(1, 0).

A'(1, −3), B'(4, −3), C'(4, 0) and D'(1, 0)

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', D → D': right 5, down 2

Let's look back.

First: draw the shape.

Then: read the move.

Then: move each point.

Then: draw the image.

Last: check.

Answer