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IG.M17 Geometric Transformations: Reflection, Rotation, Enlargement and Translation

EDEXCEL 4MA1 · Calculator allowed · about 45 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Draw the image of triangle ABC with A(1,1), B(4,1) and C(1,3) after reflection in the line y = x on the coordinate grid. Give the coordinates of A', B' and C'.

(Total for Question 1 is 3 marks)

Find the image of the point P(3, -2) after a rotation of 90 degrees anticlockwise about the origin, for the coordinate geometry context.

(Total for Question 2 is 3 marks)

Describe fully the single transformation which is equivalent to first rotating a shape 90 degrees anticlockwise about the origin and then reflecting in the y-axis. State the type of transformation and the precise line or centre and angle.

(Total for Question 3 is 3 marks)

Find the image of point A(3, 4) under an enlargement about the centre (1, 1) with scale factor -2.5 in the coordinate plane.

(Total for Question 4 is 3 marks)

Draw the image of triangle DEF with D(-1,2), E(1,2) and F(-1,-1) after the translation by vector (4, -3). Give coordinates of D', E' and F'.

(Total for Question 5 is 3 marks)

Describe fully the single transformation equivalent to first translating by the vector (5, -2) and then rotating 180 degrees about the point (2, 3). State the type, centre and angle.

(Total for Question 6 is 3 marks)

Find the image of point Q(-2, 5) after reflection in the line x = 1, in the coordinate geometry setting.

(Total for Question 7 is 3 marks)

Describe fully the single transformation equivalent to first reflecting in the x-axis (y = 0) and then rotating 90 degrees clockwise about the origin. State the transformation type and the exact line or centre and angle.

(Total for Question 8 is 3 marks)

Find the image of point R(2, 7) after an enlargement with centre (0, 0) and scale factor 1/2, as a fractional enlargement in the coordinate plane.

(Total for Question 9 is 3 marks)

Draw the image of the triangle GHI with G(0,0), H(3,0), I(0,3) after a rotation of 270 degrees anticlockwise (which is equivalent to 90 degrees clockwise) about the origin. Give coordinates of G', H' and I'.

(Total for Question 10 is 3 marks)

Find the image of point S(5, -1) after a combined transformation: first translate by ( -3, 2 ) then reflect in the line y = -1. Give S' coordinates.

(Total for Question 11 is 3 marks)

Describe fully the single transformation equivalent to reflecting in the line y = x and then reflecting in the line y = -x. State type and exact lines or centre and angle if applicable.

(Total for Question 12 is 3 marks)

Find the image of point T( -1/2, 4 ) under a rotation of 180 degrees about the point (2, 1). Give exact coordinates.

(Total for Question 13 is 3 marks)

A quadrilateral has vertices U(2,1), V(5,1), W(5,4) and X(2,4). Find the image of this quadrilateral after an enlargement with centre (2,1) and scale factor 2. Give coordinates of U', V', W' and X'.

(Total for Question 14 is 3 marks)

Mark scheme · IG.M17 Geometric Transformations: Reflection, Rotation, Enlargement and Translation

Question 1

M1 Uses reflection rule for y = x, e.g. swaps coordinates or shows method applied to at least one vertex
A1 A' = (1, 1) cao
A1 B' = (1, 4) and C' = (3, 1) both correct, cao
Answer: A' (1,1), B' (1,4), C' (3,1)

Question 2

M1 Applies the 90 degrees anticlockwise rule (x, y) -> (-y, x) correctly
A1 Gives image (2, 3) cao
B1 States final answer as P' = (2, 3) with coordinates correct
Answer: P' = (2, 3)

Question 3

M1 Shows composite mapping algebraically, e.g. (x, y) -> (-y, x) after rotation then -> (y, x) after reflection in y-axis
A1 Identifies the single transformation type, reflection, cao
A1 Gives the exact line: reflection in the line y = x cao
Answer: Reflection in the line y = x

Question 4

M1 Subtracts centre: shows vector from centre to A as (2, 3) or equivalent
M1 Multiplies vector by -2.5 to get (-5, -7.5) and adds back to centre, oe
A1 A' = (-4, -6.5) cao
Answer: A' = (-4, -6.5)

Question 5

M1 Adds the translation vector (4, -3) correctly to at least one vertex
A1 D' = (3, -1) cao
A1 E' = (5, -1) and F' = (3, -4) both correct, cao
Answer: D' (3,-1), E' (5,-1), F' (3,-4)

Question 6

M1 Forms composite mapping: (x,y) -> translate to (x+5, y-2) then 180 rotation gives (4 - (x+5), 6 - (y-2)) simplified to (-1 - x, 8 - y) or equivalent
M1 Matches composite form to 180 rotation formula (x,y) -> (2a - x, 2b - y) and solves for a and b
A1 States single transformation is rotation 180 degrees about centre (-1/2, 4) cao
Answer: Rotation through 180 degrees about the point (-1/2, 4)

Question 7

M1 Uses rule for reflection in vertical line x = 1, i.e. distance to the line preserved horizontally
A1 Computes image x-coordinate: reflect -2 across x=1 gives x' = 4 cao
A1 States Q' = (4, 5) cao
Answer: Q' = (4, 5)

Question 8

M1 Shows composite mapping: reflect (x,y)->(x,-y) then rotate 90 clockwise (u,v)->(v,-u) giving (x,y)->(-y,-x) or equivalent
A1 Identifies transformation as a reflection cao
A1 Gives exact line y = -x cao
Answer: Reflection in the line y = -x

Question 9

M1 Multiplies coordinates by scale factor 1/2 from centre (0,0) correctly
A1 Gives x' = 1 cao
A1 Gives R' = (1, 3.5) cao
Answer: R' = (1, 3.5)

Question 10

M1 Uses correct rotation rule for 270 anticlockwise, (x,y)->(y,-x), or equivalent
A1 G' = (0,0) cao
A1 H' = (0,-3) and I' = (3,0) both correct, cao
Answer: G' (0,0), H' (0,-3), I' (3,0)

Question 11

M1 Performs the translation: (5, -1) + (-3, 2) = (2, 1)
M1 Applies reflection in horizontal line y = -1 correctly, using vertical distance
A1 Final S' = (2, -3) cao
Answer: S' = (2, -3)

Question 12

M1 Shows composite mapping or recognises that two reflections in intersecting perpendicular lines equals a rotation through twice the angle between the lines, e.g. gives algebraic mapping (x,y) -> (-x,-y) or describes method
A1 Identifies the single transformation as a rotation cao
A1 Gives exact rotation: rotation through 180 degrees about the origin cao
Answer: Rotation through 180 degrees about the origin

Question 13

M1 Uses 180 rotation rule about (2,1): (x,y) -> (4 - x, 2 - y) or shows method of reversing vector from centre
M1 Substitutes T coordinates correctly to get (4 - (-1/2), 2 - 4) = (4.5, -2)
A1 States T' = (9/2, -2) cao
Answer: T' = (9/2, -2)

Question 14

M1 Uses enlargement from centre (2,1): vector from centre to a vertex doubled, at least applied correctly to one vertex
M1 Applies the same method to find remaining vertices consistently
A1 Gives U'(2,1), V'(8,1), W'(8,7) and X'(2,7) all correct, cao
Answer: U' (2,1), V' (8,1), W' (8,7), X' (2,7)

Geometric Transformations: Reflection, Rotation, Enlargement and Translation - Worksheets, Questions and Revision