Describe the transformation (1, 2) to (4, 1)

Step by step, with the reason for every step · Two moves in a row · Geometry

Step by step

Question: describe the move that takes P(1, 2) to P'(4, 1).

P = (1, 2)

P' = (4, 1)

Put the point on the grid

and its image.

Look at what happened to the numbers of P: P(1, 2) went to P'(4, 1).

P(1, 2) → P'(4, 1)

x went from 1 to 4: plus 3.

x: 1 → 4 is + 3

y went from 2 to 1: minus 1.

y: 2 → 1 is − 1

On the grid: right 3

then down 1.

So the rule is: (x, y) goes to (x + 3, y − 1).

(x, y) → (x + 3, y − 1)

Careful!

A translation moves every point the same way.

So check more than one point.

Careful: every point moves the same way

So the move is a translation: right 3, down 1.

translation = right 3, down 1

Let's check: the rule takes P to (4, 1).

That is P'.

Right!

P(1, 2) → (4, 1) = P'

Let's look back.

First: draw both shapes.

Then: compare P and P'.

Then: name the move.

Last: check.

Answer

translation = right 3, down 1

Try this one yourself, then check:

Describe the move that takes P(2, 4) → P'(5, 1)

Show the answer

translation right 3, down 3