Translate A(1, 1) B(4, 1) C(4, 3) D(1, 3) 2 left 5 down Step by Step

Step by step

The question

Question: translate the shape A(1, 1), B(4, 1), C(4, 3) and D(1, 3) left 2, down 5.

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

= left 2, down 5

1 Draw the shape

Put the points on the grid and join them.

2 Read the move

Left 2 means x gets 2 smaller: x − 2.

Left 2 → x − 2

Down 5 means y gets 5 smaller: y − 5.

Down 5 → y − 5

So every point (x, y) goes to (x − 2, y − 5).

(x, y) → (x − 2, y − 5)

3 Move each point

Start at A.

Go left 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 (1, 1).

Left 2: 1 minus 2 is −1.

Down 5: 1 minus 5 is −4.

So A' is (−1, −4).

A(1, 1) → (1 − 2, 1 − 5) = A'(−1, −4)

Careful!

Down makes y smaller.

So we take 5 away.

We do not add it.

Careful: not A'(1 − 2, 1 + 5) ✗

Now B: 4 minus 2 is 2.

1 minus 5 is −4.

So B' is (2, −4).

B(4, 1) → (4 − 2, 1 − 5) = B'(2, −4)

Now C: 4 minus 2 is 2.

3 minus 5 is −2.

So C' is (2, −2).

C(4, 3) → (4 − 2, 3 − 5) = C'(2, −2)

Now D: 1 minus 2 is −1.

3 minus 5 is −2.

So D' is (−1, −2).

D(1, 3) → (1 − 2, 3 − 5) = D'(−1, −2)

4 Draw the image

Join the new points.

This new shape is called the image.

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

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

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': left 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