Geometry

Transformations

Move a shape. Follow its coordinates.

Predict, test and explain

Step 1 of 3

Predict

An enlargement has scale factor 2. What happens to the shape’s area?

(xy)↦(x+3y+1)\binom{x}{y}\mapsto\binom{x + 3}{y + 1}
−10-10
−10-10
−8-8
−8-8
−6-6
−6-6
−4-4
−4-4
−2-2
−2-2
22
22
44
44
66
66
88
88
1010
1010
xx
yy

Scroll the diagram sideways to see every label.

Corresponding pointsA(−3,  0)↦A′(0,  1)A(-3,\;0)\mapsto A^{\prime}(0,\;1)lengths unchanged\text{lengths unchanged}

InvestigateWhich moves preserve lengths and angles?

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Try it in the simulation. Change one thing at a time.

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Hints, self-check and connections
Try a self-check

Fixed values, separate from the diagram controls.

Reflect the point in the y-axis. Find its image coordinates.

P=(3,−2)P=(3,-2)

Hint

Reflection in the y-axis reverses the horizontal coordinate and preserves the vertical coordinate.

Reveal answer

The reflected point has the opposite x-coordinate and the same y-coordinate.

P′=(−3,−2)P^{\prime}=(-3,-2)

Build an explanation

Hint 1

Track one vertex before following the whole shape.

Hint 2

For a translation, add the same across and up amounts to every point.

Hint 3

Check the stated centre or mirror line for other transformations; enlargement scales distances from its centre.

Worked example

This example uses fixed values, separate from the diagram controls.

Translate A = (−3, 0) by 3 across and 1 up.

  1. Add 3 to the x-coordinate: −3 + 3 = 0.
  2. Add 1 to the y-coordinate: 0 + 1 = 1.

Answer: A′ = (0, 1).

Connect this idea

Watch out: Translations add to coordinates; enlargements multiply distances from the stated centre.