Triangle ABC has vertices A(2, 2), B(6, 2) and C(2, 5). Translate the triangle by the vector (-3, 1). Write down the coordinates of A', B' and C'.
(2)
2
Point Q has coordinates (4, 3).
(a)Write down the coordinates of the image of Q after a reflection in the x-axis.(1)
(b)Write down the coordinates of the image of Q after a reflection in the y-axis.(1)
3
State the order of rotational symmetry of each shape.
(2)
4
Point A has coordinates (3, 4) and point B has coordinates (-2, 6). All rotations are about the origin O.
(a)A is rotated 90 degrees clockwise about O. Write down the coordinates of the image of A.(1)
(b)B is rotated 180 degrees about O. Write down the coordinates of the image of B.(1)
5
Shape P has vertices (2, 2), (4, 2) and (2, 3). Shape Q has vertices (5, 5), (7, 5) and (5, 6). Describe fully the single transformation that maps shape P onto shape Q.
(2)
6
Triangle DEF has vertices D(2, 3), E(5, 3) and F(2, 6). Reflect triangle DEF in the line y = x. Write down the coordinates of D', E' and F'.
(2)
7
State the order of rotational symmetry of a parallelogram that is not a rectangle.
(1)
8
Rotate point R(-5, -3) 90 degrees anticlockwise about the origin. Write down the coordinates of the image.
(2)
9
Reflect point S(6, -2) in the line y = x. Find the coordinates of the image.
(2)
10
Describe in words the single transformation that maps the point (x, y) to (-x, y) for every point on a shape.
(1)
11
Describe in words the single transformation that maps the point (x, y) to (-x, -y) for every point on a shape.
(1)
12
A shape is translated by the vector (4, -6) to form its image. A vertex of the shape is at (-1, 8). Find the coordinates of the corresponding vertex on the image.
(2)
13
Triangle A(3, 5), B(6, 5), C(3, 8) is first rotated 90 degrees anticlockwise about the origin, then reflected in the x-axis. Give the final coordinates of A', B' and C'.
(3)
14
Shape M has vertices (1, 2), (4, 2) and (1, 5). Shape N has vertices (-2, 1), (-2, 4) and (-5, 1). Describe fully the single transformation that maps shape M onto shape N.
(3)
15
A logo designer rotates point L(7, 2) about the point (2, 2) by 90 degrees clockwise. Find the coordinates of the image L'.
(3)
16
State the order of rotational symmetry of a regular octagon, and the size of the angle turned between each match.
(3)
17
A triangle has vertices (2, -1), (6, -1) and (6, 2). First reflect the triangle in the y-axis, then rotate the result 90 degrees clockwise about the origin. Give the final coordinates of the three vertices.
(4)
18
Jordan says: "A shape and its enlargement by scale factor -1 about the origin are always congruent." Is Jordan correct? Give a reason.
(3)
Mark scheme · KS3.M-G3D Geometry: Transformations: Fluency and Exam Drill
Question 1
M1 adds the vector to each vertex, showing at least one correct addition
A1 A'(-1, 3), B'(3, 3), C'(-1, 6) cao
Answer: A'(-1, 3), B'(3, 3), C'(-1, 6)
Question 2
(a) B1 (4, -3) cao
(a) Answer: (4, -3)
(b) B1 (-4, 3) cao
(b) Answer: (-4, 3)
Question 3
M1 at least two of the three orders correct
A1 all three correct: rectangle (not a square) = 2, regular hexagon = 6, scalene triangle = 1 cao
M1 rotate 90 degrees anticlockwise: (x, y) -> (-y, x) shown for at least one vertex
M1 reflect in x-axis: show y -> -y for at least one rotated vertex
A1 final vertices A'(-5, -3), B'(-5, -6), C'(-8, -3) cao
Answer: A'(-5, -3), B'(-5, -6), C'(-8, -3)
Question 14
M1 checks a mapping rule against more than one vertex, e.g. tests (x, y) -> (-y, x)
A1 states rotation of 90 degrees anticlockwise
A1 states centre (0, 0) cao
Answer: Rotation of 90 degrees anticlockwise about the origin (0, 0)
Question 15
M1 finds the vector from the centre (2, 2) to L: (5, 0)
A1 applies the 90 degrees clockwise rule (x, y) -> (y, -x) to the vector: (0, -5)
A1 L' = centre + rotated vector = (2, -3) cao
Answer: (2, -3)
Question 16
M1 identifies order of rotational symmetry equals the number of sides
A1 order = 8 cao
A1 angle = 360/8 = 45 degrees cao
Answer: Order 8; angle between matches = 45 degrees
Question 17
M1 reflect in y-axis: x -> -x shown for at least one vertex
M1 rotate 90 degrees clockwise: (x, y) -> (y, -x) shown for at least one reflected vertex
M1 applies both steps to the remaining vertices correctly
A1 final vertices (-1, 2), (-1, 6), (2, 6) cao (in any order)
Answer: (-1, 2), (-1, 6), (2, 6)
Question 18
M1 recognises that the size of the scale factor (its absolute value) is 1
M1 explains that scale factor -1 multiplies every distance from the centre by 1 but reverses direction, which is equivalent to a rotation of 180 degrees about the origin
A1 concludes Jordan is correct because the image has exactly the same side lengths and angles as the original, so it is congruent
Answer: Yes. Scale factor -1 has size 1, so all lengths are unchanged; the image is a 180 degree rotation of the original about the origin, which is congruent to it.