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11+ · Coordinates and Transformations

EP.M119 Coordinates, Reflection and Translation

GL ASSESSMENT GL-11PLUS-MATHS · Calculators not allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Point A is at (3, -7). What is the y-coordinate of A?

A) 3
B) -7
C) 7
D) -3
E) 0

(Total for Question 1 is 1 mark)

Write the coordinates of point B if B is 4 units left of the origin and 3 units above it.

(Total for Question 2 is 1 mark)

Which of the following points lies in quadrant III?

A) (2, -5)
B) (-4, 3)
C) (-3, -2)
D) (0, -1)
E) (5, 0)

(Total for Question 3 is 1 mark)

Points A and B are A(2, -1) and B(-3, 4). Work out the midpoint of AB.

(Total for Question 4 is 2 marks)

Reflect point C(-5, 2) in the x-axis. Give the coordinates of the image.

(Total for Question 5 is 1 mark)

Reflect point D(4, -7) in the y-axis. Give the coordinates of the image.

(Total for Question 6 is 1 mark)

Translate point E(1, -3) by the vector (4, 5). Give the coordinates of the image.

(Total for Question 7 is 1 mark)

Point F is at (-2, 6). (a) Reflect F in the x-axis. (b) Then translate the image by (-3, -2). Give the coordinates after each step.

(a)Reflect F in the x-axis.(1)

(b)Translate the result by (-3, -2).(1)

(Total for Question 8 is 2 marks)

Triangle T has vertices A(1,1), B(4,1), C(1,3). Translate the triangle by (-2, -1). Give the coordinates of A', B' and C'.

(Total for Question 9 is 2 marks)

Which translation maps (2, 3) to (-1, -1)?

A) (-3, -4)
B) (3, 4)
C) (-1, -2)
D) (-3, 4)
E) ( -4, -1)

(Total for Question 10 is 1 mark)

Point P moves from (-4, 2) to Q(1, -1). Give the translation vector that moves P to Q.

(Total for Question 11 is 2 marks)

Point G is at (3, -5). It is reflected in the x-axis, then translated by (-2, 3). Work out the final coordinates.

(Total for Question 12 is 2 marks)

Point H is at (-2, 0). Which reflection will move H to (2, 0)?

A) Reflect in the x-axis
B) Reflect in the y-axis
C) Reflect in the line y = x
D) Translate by (4, 0)
E) Rotate 180 degrees about the origin

(Total for Question 13 is 1 mark)

A square has vertices (2,2), (5,2), (5,5), (2,5). The square is reflected in the y-axis and then translated by (-1, 0). Find the coordinates of the image of the vertex (2,5).

(Total for Question 14 is 2 marks)

Triangle with vertex A(-1, 2) is reflected in the x-axis to form A1, then A1 is translated by (4, -1) to form A2. Find the coordinates of A2.

(Total for Question 15 is 2 marks)

A point (x, y) is reflected in the x-axis and then in the y-axis. The final image is (6, -4). What were the original coordinates?

(Total for Question 16 is 2 marks)

A point starts at (1, 1). It is translated by (2, -1), then reflected in the y-axis, then translated by (-3, 5). What are the final coordinates?

(Total for Question 17 is 2 marks)

Point P is at (4, -1). It is reflected in the line y = 0 then reflected in the line x = 1. Find the final coordinates of the image.

(Total for Question 18 is 2 marks)

Mark scheme · EP.M119 Coordinates, Reflection and Translation

Question 1

B1 correct option B (-7) cao
Answer: B) -7 (the y-coordinate is -7). (1 mark.) A pupil who picks A or D has confused x and y; C has wrong sign; E is wrong column value only.)

Question 2

B1 (-4, 3) cao
Answer: (-4, 3)

Question 3

B1 correct option C ((-3, -2)) cao
Answer: C) (-3, -2). Quadrant III has x < 0 and y < 0. (Options A and D have x ≥ 0; B has y > 0; E lies on the x-axis.)

Question 4

M1 Correct method: average x-values and average y-values ( (2 + -3)/2, (-1 + 4)/2) seen
A1 (-0.5, 1.5) cao
Answer: (-0.5, 1.5). Working: x-mid = (2 + (-3))/2 = -1/2 = -0.5; y-mid = (-1 + 4)/2 = 3/2 = 1.5.

Question 5

B1 (-5, -2) cao
Answer: (-5, -2). Reflection in the x-axis changes y to its negative; x stays the same.

Question 6

B1 (-4, -7) cao
Answer: (-4, -7). Reflection in the y-axis changes x to its negative; y stays the same.

Question 7

B1 (5, 2) cao
Answer: (5, 2). Work: (1 + 4, -3 + 5) = (5, 2).

Question 8

(a) B1 (-2, -6) cao
(a) Answer: (-2, -6)
(b) B1 (-5, -8) cao
(b) Answer: (-5, -8)

Question 9

M1 Evidence of translation applied to at least one vertex, e.g. (1,1) -> (-1,0) or equivalent
A1 A'(-1,0), B'(2,0), C'(-1,2) cao
Answer: A'(-1, 0), B'(2, 0), C'(-1, 2). Work: add (-2, -1) to each vertex.

Question 10

B1 correct option A ((-3, -4)) cao
Answer: A) (-3, -4). Work: (-1 - 2, -1 - 3) = (-3, -4). Distractors: B is sign error; C arithmetic error; D changes y sign incorrectly; E swaps components.

Question 11

M1 Method: difference Q - P seen, e.g. (1 - (-4), -1 - 2) or equivalent
A1 (5, -3) cao
Answer: (5, -3). Work: x increases by 5, y decreases by 3.

Question 12

M1 Reflect then translate method seen, e.g. (3, -5) -> (3, 5) -> (1, 8)
A1 (1, 8) cao
Answer: (1, 8). Reflection in x-axis gives (3, 5); adding (-2, 3) gives (1, 8).

Question 13

B1 correct option B (reflect in the y-axis) cao
Answer: B) Reflect in the y-axis. Reflection in y-axis changes (-2,0) to (2,0). A would give (-2,0) -> (-2,0) as y=0 unchanged; C swaps coordinates; D gives (2,0) only if translate by (4,0) from (-2,0) but that is also correct numerically; however translation is not a reflection so B is correct reflection. (Note: D would move H to (2,0) but the question asks which reflection.)

Question 14

M1 Reflect then translate method applied to the vertex, e.g. (2,5) -> (-2,5) -> (-3,5)
A1 (-3, 5) cao
Answer: (-3, 5). Reflect (2,5) in y-axis to get (-2,5), then add (-1,0) to get (-3,5).

Question 15

M1 Reflect then translate method shown, e.g. (-1,2) -> (-1,-2) -> (3,-3)
A1 (3, -3) cao
Answer: (3, -3). Reflection in x-axis gives (-1, -2); adding (4, -1) gives (3, -3).

Question 16

M1 Method: track sign changes or reverse reflections, e.g. after two reflections image is (-x, -y) so set equal to (6, -4)
A1 (-6, 4) cao
Answer: (-6, 4). Reason: reflection in x then y gives (-x, -y) = (6, -4) so x = -6, y = 4.

Question 17

M1 Method showing sequence applied correctly, e.g. (1,1)->(3,0)->(-3,0)->(-6,5)
A1 (-6, 5) cao
Answer: (-6, 5). Steps: (1,1)+(2,-1) = (3,0); reflect in y-axis -> (-3,0); add (-3,5) -> (-6,5).

Question 18

M1 Method: reflect in y=0 to change sign of y, then reflect in x=1 using x_new = 2*1 - x
A1 (-2, 1) cao
Answer: (-2, 1). Work: reflect in y=0 gives (4,1). Reflect in x=1: x' = 2*1 - 4 = -2, y' = 1.

Coordinates, Reflection and Translation - Worksheets, Questions and Revision