TRANSFORMATIONS-1

1)

(a) Rotate the F through 90˚ anticlockwise about the point O. Draw the new F. [2]

(b) Enlarge the square by a scale factor of 4, using the point C as the centre of enlargement.

[2]

(c) Write down the area of the enlarged square. [1]

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2)

(a) Describe fully the single transformation which maps triangle A onto triangle B. [2]

(b) Find the 2 × 2 matrix which represents this transformation. [2]

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3)

(a) Enlarge, shape A using scale factor 2 and P as the centre of enlargement.

Write A1 in the enlarged shape. [2]

 3 
(b) Translate shape B using the vector   . Write B1 in the translated shape. [2]

 2

(c) Rotate shape C 90˚ clockwise about the point labelled Q.

Write C1 in the rotated shape. [2]

(d) Reflect shape D in the line RS. Write D1 in the reflected shape. [2]

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 (e) Describe fully the single transformation which maps

(i) shape A1 onto shape A,

Answer (e)(i) ............................................................................................... [2]

(ii) shape B1 onto shape B.

Answer (e)(ii) ............................................................................................... [2]

4)

(a) (i) Draw the reflection of triangle A in the x - axis. Label it B. [2]

(ii) Draw the reflection of triangle B in the line y = -4. Label it C. [2]

(iii) Describe fully the single transformation which maps triangle A onto triangle C. [2]

(b) (i) Draw the rotation of triangle A about the origin through 180". Label it D. [2]

(ii) Describe fully the single transformation which maps triangle D onto triangle B.

(c) Draw the enlargement of triangle A, with centre of enlargement P(8, 1) and

scale factor 2. Label it E. [2]

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5)

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  5 
(i) Translate triangle LMN using the vector   . [2]
  2
(ii) Describe fully the transformation which maps triangle LMN onto triangle PQR.

Answer (c)(ii) ........................................................................................................... . [2]

(iii) Enlarge triangle LMN with centre of enlargement O and scale factor 3. [3]

6) (a) Enlarge the quadrilateral OABC with centre of enlargement O and scale factor 3.

(b) Write down the special name of the quadrilateral OABC. [1]

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7)

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 (a) Describe fully the single transformation which maps

(i) triangle A onto triangle B, [2]

(ii) triangle A onto triangle C, [3]

(iii) triangle A onto triangle D. [3]

(b) On the grid above, draw

(i) the reflection of triangle B in the line l, [2]

(ii) the rotation of triangle E about the point P through 90° clockwise.

[2]

8)

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 (a) On the grid, draw the following transformations.

(i) The rotation of S, 90° clockwise, about the point P. Label it A. [2]

  4
(ii) The translation of S by the vector   . Label it B. [2]
  3
(iii) The enlargement of S with centre (0, 0) and scale factor 2. Label it C. [3]

(iv) The reflection of S in the line y = 4. Label it D. [3]

(b) Write down the vector which translates B back to the original position of S. [1]

9)

(a) Describe fully the transformation which maps

(i) shape L onto shape M, [2]

(ii) shape L onto shape N. [2]

  7
(b) (i) Translate shape L using the vector   . [2]
  4

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 1
(ii) Enlarge shape L with centre of enlargement 0, scale factor [2]
2

10) (a)

Draw the shear of the shaded square with the x-axis invariant and the point (0, 2)

mapping onto the point (3, 2). [2]

(b)

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 (i) Draw the one-way stretch of the shaded square with the x-axis invariant and the point

(0, 2) mapping onto the point (0, 6). [2]

(ii) Write down the matrix of this stretch. [1]

11)

(a) Draw accurately the image of triangle T under the following transformations.

  3
(i) Translate triangle T by the vector   . Label it P. [2]
 4 
(ii) Reflect triangle T in the line x = 8. Label it Q. [2]

(iii) Rotate triangle T about the point A through 90° anti-clockwise.

Label it R. [2]

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 (iv) Enlarge triangle T with centre of enlargement A and scale factor 2.

Label it S. [2]

(b) Describe fully the single transformation which maps

(i) triangle P onto triangle T, [2]

(i) triangle S onto triangle T. [3]

(c) The rectangle DEFG is rotated onto the rectangle KLMN, with D mapped onto K.

Write down

(i) the angle of the rotation, [1]

(ii) the coordinates of the centre of the rotation. [2]

12)

 x
(a) Triangle ABD is translated onto triangle EGF by the vector   .
 
y

Write down the value of x and the value of y. [2]

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 (b) Describe fully the single transformation which maps triangle ABD onto

(i) triangle CDB, [3]

(ii) triangle HBF. [3]

(c) (i) Work out the area of triangle ABD. [1]

(ii) What is the ratio area of triangle ABD : area of triangle HBF?

Give your answer in its lowest terms. [2]

(d) Find the gradient of the line BF. [2

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