AI generatedGeometry and measuresKey Stage 3

Finding the centre of enlargement

Finding the centre of enlargement.

  • Match corresponding vertices before describing a transformation.
  • Reflection: mirror line. Rotation: centre, angle and direction. Translation: vector.
  • Enlargement: centre and scale factor. Apply combined transformations in the stated order.

Example 1

Find the centre of enlargement.

Black: original. Blue: image.−2246−22460ABCA′B′C′
Black: original. Blue: image.
Centre (-1, -1).
Black: original. Blue: image.−2246−22460ABCA′B′C′O
Black: original. Blue: image.

Draw lines through matching vertices and extend them back to their common intersection. Compare corresponding side lengths to find the scale factor.

Example 2

Find the centre of enlargement.

Black: original. Blue: image.−2246810−22468100ABCA′B′C′
Black: original. Blue: image.
Centre (0, -1).
Black: original. Blue: image.−2246810−22468100ABCA′B′C′O
Black: original. Blue: image.

Draw lines through matching vertices and extend them back to their common intersection. Compare corresponding side lengths to find the scale factor.

Your turn

Question 1

Find the centre of enlargement.

Black: original. Blue: image.−22468−224680ABCA′B′C′
Black: original. Blue: image.
Check answer
Centre (1, -1).
Black: original. Blue: image.−22468−224680ABCA′B′C′O
Black: original. Blue: image.

Draw lines through matching vertices and extend them back to their common intersection. Compare corresponding side lengths to find the scale factor.

Question 2

Find the centre of enlargement.

Black: original. Blue: image.−2246810−22468100ABCA′B′C′
Black: original. Blue: image.
Check answer
Centre (-1, 0).
Black: original. Blue: image.−2246810−22468100ABCA′B′C′O
Black: original. Blue: image.

Draw lines through matching vertices and extend them back to their common intersection. Compare corresponding side lengths to find the scale factor.

Question 3

Find the centre of enlargement.

Black: original. Blue: image.−22468−224680ABCA′B′C′
Black: original. Blue: image.
Check answer
Centre (0, 0).
Black: original. Blue: image.−22468−224680ABCA′B′C′O
Black: original. Blue: image.

Draw lines through matching vertices and extend them back to their common intersection. Compare corresponding side lengths to find the scale factor.

Question 4

Find the centre of enlargement.

Black: original. Blue: image.−224681012−2246810120ABCA′B′C′
Black: original. Blue: image.
Check answer
Centre (1, 0).
Black: original. Blue: image.−224681012−2246810120ABCA′B′C′O
Black: original. Blue: image.

Draw lines through matching vertices and extend them back to their common intersection. Compare corresponding side lengths to find the scale factor.

Question 5

Find the centre of enlargement.

Black: original. Blue: image.−2246−22460ABCA′B′C′
Black: original. Blue: image.
Check answer
Centre (-1, 1).
Black: original. Blue: image.−2246−22460ABCA′B′C′O
Black: original. Blue: image.

Draw lines through matching vertices and extend them back to their common intersection. Compare corresponding side lengths to find the scale factor.

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