4MA1/1F Jun 2023, Question 19: Translation

Part (a) · 3 marks

Triangle A is translated onto triangle B; determine the values of d, e and f from the given vertices.

1. 1The top vertex moves from (−7, 2) to (6, 12)
2. 26 − (−7) = 13 and 12 − 2 = 10, so the translation is 13 right and 10 up
3. 3d = −5 + 10 = 5
4. 4e = −3 + 10 = 7
5. 5f = 9 − 13 = −4

Answerd = 5, e = 7, f = −4

Part (b) · 3 marks

State the single transformation, described fully, that takes shape P onto shape Q.

1. 1Shape Q is three times as tall and three times as wide as shape P, so the scale factor is 3
2. 2Joining each vertex of P to the matching vertex of Q, the lines all meet at (0, 2)
3. 3So it is an enlargement, scale factor 3, centre (0, 2)

AnswerEnlargement, scale factor 3, centre (0, 2)

Part (c) · 2 marks

Rotate shape P 90° clockwise about the point (3, 5) and label the result R.

1. 1A 90° clockwise turn about (3, 5) sends (x, y) to (3 + y − 5, 5 − x + 3)
2. 2(2, 5) goes to (3, 6)
3. 3(2, 3) goes to (1, 6)
4. 4(3, 3) goes to (1, 5)
5. 5(3, 2) goes to (0, 5)

AnswerR at (3, 6), (1, 6), (1, 5), (0, 5)

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