Instructions
Welcome! This worksheet will help you practice two important types of transformations: reflections and rotations.
- A reflection is like flipping a shape over a line. This line is called the line of reflection (like the x-axis or y-axis).
- A rotation is like turning a shape around a fixed point, called the center of rotation. We will use the origin (0, 0) as our center of rotation.
Read each question carefully. For questions involving coordinates, remember that they are always written as (x, y).
Part 1: Objective Questions
Choose the best answer for each question.
- Which of these transformations is like a mirror image?
A) Rotation
B) Reflection
C) Slide - If you reflect the point P(3, 4) across the x-axis, what are the new coordinates?
A) (-3, 4)
B) (3, -4)
C) (-3, -4) - If you reflect the point Q(-2, 5) across the y-axis, what are the new coordinates?
A) (2, 5)
B) (-2, -5)
C) (2, -5) - A rotation turns a shape around a fixed point. What is this point called?
A) The origin
B) The center of rotation
C) The axis - True or False: Reflecting a shape changes its size.
A) True
B) False - A 90° clockwise rotation is the same as a...
A) 180° rotation
B) 90° counter-clockwise rotation
C) 270° counter-clockwise rotation - What are the coordinates of point A(6, 2) after a 180° rotation around the origin (0,0)?
A) (-6, -2)
B) (6, -2)
C) (-2, 6) - A triangle is in the top-right quadrant. After a reflection across the y-axis, which quadrant will it be in?
A) Top-left
B) Bottom-right
C) Bottom-left - True or False: Rotating a shape changes its orientation (which way it's facing).
A) True
B) False - The point B(8, -1) is reflected across the x-axis. What are the new coordinates?
A) (-8, -1)
B) (8, 1)
C) (-8, 1) - What are the coordinates of point C(-4, -9) after a reflection across the y-axis?
A) (4, 9)
B) (-4, 9)
C) (4, -9) - What happens to the y-coordinate when a point is reflected across the x-axis?
A) It stays the same.
B) Its sign flips (e.g., 5 becomes -5).
C) It becomes zero. - Point D(5, 3) is rotated 90° clockwise around the origin. What are its new coordinates?
A) (-3, 5)
B) (3, -5)
C) (-5, -3) - Point E(-2, 7) is rotated 90° counter-clockwise around the origin. What are its new coordinates?
A) (-7, -2)
B) (7, 2)
C) (2, 7) - Which rotation will move a shape from the top-right quadrant to the bottom-left quadrant?
A) 90° clockwise
B) 180°
C) 270° clockwise - What happens to the x-coordinate when a point is reflected across the y-axis?
A) It stays the same.
B) It becomes the y-coordinate.
C) Its sign flips (e.g., 2 becomes -2). - The point F(-5, -6) is reflected across the x-axis. The new point is F'. F' is then reflected across the y-axis. What are the final coordinates?
A) (-5, -6)
B) (5, 6)
C) (5, -6) - A shape that has "rotational symmetry" looks the same after being...
A) Reflected.
B) Rotated less than a full 360°.
C) Made bigger. - A 360° rotation around the origin results in the shape...
A) Being upside down.
B) Being in the opposite quadrant.
C) Being back in its original position. - The point G(0, 5) is on the y-axis. What happens when it is reflected across the y-axis?
A) Its coordinates become (5, 0).
B) Its coordinates become (0, -5).
C) It does not move.
Part 2: Subjective Questions
Write your answers in the space provided. Show the new coordinates clearly.
- A point is located at K(7, -3). What are the coordinates of K' after it is reflected across the x-axis?
Answer: _______________
- A point is located at L(-5, 9). What are the coordinates of L' after it is reflected across the y-axis?
Answer: _______________
- A triangle has vertices at A(1, 2), B(5, 2), and C(3, 6). What are the coordinates of its image (A', B', C') after a reflection across the x-axis?
A': _______ B': _______ C': _______
- A square has vertices at P(2, 3), Q(6, 3), R(6, 7), and S(2, 7). What are the coordinates of its image (P', Q', R', S') after a reflection across the y-axis?
P': _______ Q': _______ R': _______ S': _______
- Point M(4, 8) is rotated 90° clockwise around the origin (0, 0). What are the coordinates of M'?
Answer: _______________
- Point N(-3, 2) is rotated 180° around the origin (0, 0). What are the coordinates of N'?
Answer: _______________
- A line segment has endpoints at D(-1, -4) and E(-1, -8). What are the new endpoints (D' and E') after a 90° counter-clockwise rotation around the origin?
D': _______ E': _______
- A rectangle has vertices at W(1,1), X(5,1), Y(5,3), and Z(1,3). What are the new vertices (W', X', Y', Z') after a 180° rotation around the origin?
W': _______ X': _______ Y': _______ Z': _______
- A transformation moves point F(5, 2) to point F'(-5, 2). What specific reflection caused this change?
Answer: Reflection across the _______________
- A transformation moves point G(3, -4) to point G'(-3, 4). What specific rotation caused this change?
Answer: A _______________ rotation around the origin.
Answer Key
Part 1: Objective Questions
- B) Reflection
- B) (3, -4)
- A) (2, 5)
- B) The center of rotation
- B) False
- C) 270° counter-clockwise
- A) (-6, -2)
- A) Top-left
- A) True
- B) (8, 1)
- C) (4, -9)
- B) Its sign flips (e.g., 5 becomes -5).
- B) (3, -5)
- A) (-7, -2)
- B) 180°
- C) Its sign flips (e.g., 2 becomes -2).
- B) (5, 6)
- B) Rotated less than a full 360°.
- C) Being back in its original position.
- C) It does not move.
Part 2: Subjective Questions
- Answer: (7, 3)
- Answer: (5, 9)
- A': (1, -2) B': (5, -2) C': (3, -6)
- P': (-2, 3) Q': (-6, 3) R': (-6, 7) S': (-2, 7)
- Answer: (8, -4)
- Answer: (3, -2)
- D': (4, -1) E': (8, -1)
- W': (-1, -1) X': (-5, -1) Y': (-5, -3) Z': (-1, -3)
- Answer: Reflection across the y-axis
- Answer: A 180° rotation around the origin.