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KS3 · Geometry and Measures

KS3.M-G17 Transformations: Translation and Enlargement

AQA KS3.M-G17 · Calculators not allowed · about 60 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write down the column vector that describes a translation 4 squares to the right and 2 squares up.

(1)

Write down the column vector that describes a translation 3 squares to the left and 5 squares down.

(1)

A translation is given by the column vector (0, 6). Describe this translation in words.

(1)

Carry out the addition of the two column vectors. (2, -3) + (-1, 4).

(2)

A triangle has vertices at A(1, 2), B(3, 2) and C(2, 4). Translate the triangle by the vector (4, -1). Write the new coordinates of A, B and C.

(2)

On a square grid, shape S is translated by the vector (-2, 3) to form shape T. If a vertex of S is at (6, 1), what are the coordinates of the corresponding vertex of T?

(2)

Enlarge the triangle with vertices (1, 1), (3, 1) and (1, 4) by scale factor 2 about the origin (0, 0). Write the coordinates of the image.

(3)

Enlarge the triangle with vertices (2, -1), (5, 3) and (2, 3) by scale factor 3 about the point (1, 0). Give the coordinates of the image.

(3)

A square with corners at (2, 2), (5, 2), (5, 5), (2, 5) is enlarged by scale factor 1/2 about the origin. Give the coordinates of the image.

(2)

Enlarge point P(4, 6) by scale factor 4 about the point (2, 1). Work out the image P'.

(2)

A triangle with vertices (2, 2), (4, 2) and (2, 5) is first translated by (3, -1) then enlarged by scale factor 2 about the origin. Find the coordinates after both transformations.

(3)

Enlarge the rectangle with corners (1, 1), (5, 1), (5, 3), (1, 3) by scale factor 0.5 about the point (1, 1). Give the coordinates of the image.

(3)

The point Q is at (-1, 4). It is translated by (5, -6) then enlarged by scale factor 2 about the origin. Find the final coordinates.

(2)

A triangle has vertices at (2, 0), (4, 0) and (2, 3). It is enlarged by scale factor 3 about the point (2, 0). Give the coordinates of the image.

(3)

A pentagon has a vertex at (0, 2). After enlargement by scale factor 2 about the origin the image of that vertex is (0, 4). If the original pentagon is then translated by (1, -3), what is the coordinate of that translated vertex?

(2)

Sam says: "Enlarging a shape by scale factor 1 about any point always gives the same shape in the same place." Is Sam correct? Give a reason.

(3)

A triangle has vertices A(1, 2), B(4, 2) and C(1, 5). A enlargement with scale factor 1.5 about the origin maps A to A'. Find the coordinates of A', B' and C'. (Give any decimal answers to one decimal place if needed.)

(3)

Stretch question. A shape is enlarged by scale factor 2 about the point (3, -1). One vertex of the original shape is at (7, 5) and the corresponding vertex of the image is at (11, 9). Verify these coordinates and explain whether these two points are consistent with enlargement by scale factor 2 about (3, -1). Show your working.

(4)

Mark scheme · KS3.M-G17 Transformations: Translation and Enlargement

Question 1

B1 Correct column vector (4, 2) cao
Answer: [4, 2] (or column vector (4, 2))

Question 2

B1 Correct column vector (-3, -5) cao
Answer: [-3, -5] (or column vector (-3, -5))

Question 3

B1 Description equivalent to "6 squares up" or "up 6" cao
Answer: Translate up 6

Question 4

M1 Adds components correctly: (2 + -1, -3 + 4) or equivalent
A1 Gives final vector (1, 1) cao
Answer: [1, 1] (or column vector (1, 1))

Question 5

M1 Adds vector to each point correctly, showing at least one correct addition
A1 All three coordinates correct: A'(5,1), B'(7,1), C'(6,3) cao
Answer: A'(5, 1), B'(7, 1), C'(6, 3)

Question 6

M1 Applies translation to coordinates (6 + -2, 1 + 3) or equivalent
A1 Gives (4, 4) cao
Answer: (4, 4)

Question 7

M1 Multiples coordinates by 2 for at least one point correctly
M1 Shows method for other points or lists transformed coordinates
A1 All three correct: (2,2), (6,2), (2,8) cao
Answer: (2, 2), (6, 2), (2, 8)

Question 8

M1 Subtracts centre (1,0) from a point, multiplies by 3 and adds centre for at least one point
M1 Applies method to remaining points or shows clear working
A1 All three image coordinates correct: (4, -3), (13, 9), (4, 9) cao
Answer: (4, -3), (13, 9), (4, 9)

Question 9

M1 Multiplies each coordinate by 1/2 or 0.5
A1 Gives (1,1), (2.5,1), (2.5,2.5), (1,2.5) cao
Answer: (1, 1), (2.5, 1), (2.5, 2.5), (1, 2.5)

Question 10

M1 Subtracts centre (2,1): vector (2,5), multiplies by 4 to get (8,20) then adds centre
A1 P'(10,21) cao
Answer: P'(10, 21)

Question 11

M1 Applies translation to each point or shows one correct translated point
M1 Then multiplies translated coordinates by 2 about origin correctly
A1 Final coordinates correct: (10,2), (14,2), (10,8) cao
Answer: (10, 2), (14, 2), (10, 8)

Question 12

M1 Subtracts centre (1,1) from a corner: e.g. (0,0), (4,0), (4,2), (0,2) then multiplies by 0.5
M1 Adds centre back to get image coordinates for points other than the centre
A1 Gives images: (1,1), (3,1), (3,2), (1,2) cao
Answer: (1, 1), (3, 1), (3, 2), (1, 2)

Question 13

M1 Translates: (-1+5, 4-6) = (4, -2), then multiplies by 2
A1 Final point (8, -4) cao
Answer: (8, -4)

Question 14

M1 Takes (2,0) as centre, subtracts centre for other points: (0,0), (2,0), (0,3)
M1 Multiplies by 3 and adds centre back correctly
A1 Image coordinates: (2,0), (8,0), (2,9) cao
Answer: (2, 0), (8, 0), (2, 9)

Question 15

M1 Applies translation to original vertex (0,2): (0+1,2-3)
A1 Gives (1, -1) cao
Answer: (1, -1)

Question 16

M1 States whether correct or not: correct that shape is unchanged in size
M1 Explains that scale factor 1 means distances from centre are multiplied by 1 so points do not move
A1 Concludes that the shape remains in the same place and size; wording equivalent to this earns the mark
Answer: Yes. Scale factor 1 multiplies all distances from the centre by 1 so every point stays where it is; the shape is unchanged.

Question 17

M1 Multiplies coordinates by 1.5 for at least one point correctly
M1 Applies to remaining points or shows method
A1 Gives A'(1.5, 3.0), B'(6.0, 3.0), C'(1.5, 7.5) with acceptable rounding
Answer: A'(1.5, 3.0), B'(6.0, 3.0), C'(1.5, 7.5)

Question 18

M1 Finds vector from centre to original: (7-3, 5-(-1)) = (4, 6) or equivalent
M1 Multiplies that vector by 2 to get (8, 12)
M1 Adds centre back: (3+8, -1+12) = (11, 11) or shows this calculation
A1 Conclusion that image should be (11, 11), so given image (11, 9) is not consistent with scale factor 2 about (3, -1); explanation given
Answer: Not consistent. Correct image would be (11, 11), so (11, 9) is incorrect for scale factor 2 about (3, -1).

Transformations: Translation and Enlargement - Worksheets, Questions and Revision