Unit 6 · Class 7 IB MYP · MCQ Test
Transformations MCQ Test — Class 7 IB MYP
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Transformations — MCQ Questions
1A point P has coordinates (3, -2). It is translated by the vector \(\begin{pmatrix} -4 \\ 5 \end{pmatrix}\). What are the new coordinates of P'?
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Answer: (-1, 3)
Hint: To translate a point by a vector, add the x-component of the vector to the x-coordinate of the point, and the y-component to the y-coordinate.
Solution:
Identify the original coordinates of P: (3, -2). — P = (x, y) = (3, -2)
Identify the translation vector: \(\begin{pmatrix} -4 \\ 5 \end{pmatrix}\). — Vector = \(\begin{pmatrix} a \\ b \end{pmatrix}\) = \(\begin{pmatrix} -4 \\ 5 \end{pmatrix}\)
Apply the translation rule (x+a, y+b). — P' = (3 + (-4), -2 + 5)
Calculate the new coordinates. — P' = (-1, 3)
2A triangle with vertices A(1, 4), B(3, 1), and C(5, 4) is reflected across the x-axis. What are the coordinates of the reflected vertex A'?
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Answer: (1, -4)
Hint: When reflecting a point across the x-axis, the x-coordinate remains the same, but the y-coordinate changes its sign.
Solution:
Identify the coordinates of vertex A: (1, 4). — A = (x, y) = (1, 4)
Recall the rule for reflection across the x-axis: (x, y) → (x, -y).
Apply the rule to point A. — A' = (1, -4)
3A point Q is located at (-2, 5). What are the coordinates of Q' after a 90° clockwise rotation about the origin?
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Answer: (5, 2)
Hint: For a 90° clockwise rotation about the origin, the rule is (x, y) → (y, -x).
Solution:
Identify the coordinates of Q: (-2, 5). — Q = (x, y) = (-2, 5)
Recall the rule for a 90° clockwise rotation about the origin: (x, y) → (y, -x).
Apply the rule to point Q. — Q' = (5, -(-2))
Simplify the coordinates. — Q' = (5, 2)
4A small toy car moves from its starting position at (2, 1) to a new position at (-1, 3) on a coordinate map. Which single transformation best describes its movement?
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Answer: Translation by vector \(\begin{pmatrix} -3 \\ 2 \end{pmatrix}\)
Hint: Compare the change in x-coordinates and y-coordinates to determine the components of the translation vector.
Solution:
Identify the starting point P: (2, 1) and the ending point P': (-1, 3).
To find the translation vector \(\begin{pmatrix} a \\ b \end{pmatrix}\), calculate the change in x (a = x' - x) and the change in y (b = y' - y).
Calculate the x-component. — a = -1 - 2 = -3
Calculate the y-component. — b = 3 - 1 = 2
Form the translation vector. — Vector = \(\begin{pmatrix} -3 \\ 2 \end{pmatrix}\)
5Which of the following statements about congruence and transformations is true?
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Answer: Rotation always changes the orientation of a shape but not its size.
Hint: Recall the definition of congruence and how each type of transformation affects the properties (size, shape, orientation) of a figure.
Solution:
Analyze Option A: Reflection preserves size and shape, only changing orientation. So, A is false.
Analyze Option B: Rotation preserves size and shape, changing only position and orientation. This statement is true.
Analyze Option C: Translation preserves size, shape, and orientation, only changing position. So, C is false.
Analyze Option D: All three rigid transformations (translation, reflection, rotation) result in an image congruent to the original shape. So, D is false.
6Alex reflected the point R(4, -3) across the y-axis and got R'(-4, -3). His friend, Ben, says Alex made a mistake. Which statement describes Alex's mistake, if any?
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Answer: Alex did not make a mistake, R'(-4, -3) is correct.
Hint: Remember the rule for reflecting a point across the y-axis: (x, y) → (-x, y).
Solution:
Identify the original point R: (4, -3). — R = (x, y) = (4, -3)
Recall the rule for reflection across the y-axis: (x, y) → (-x, y).
Apply the rule to point R. — R' = (-4, -3)
Compare Alex's result with the correct application of the rule. Alex's result R'(-4, -3) is correct.
7During a navigation exercise, a drone flies from a control point at (5, 7) to a target at (2, 4). Which translation vector represents the drone's movement?
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Answer: \(\begin{pmatrix} -3 \\ -3 \end{pmatrix}\)
Hint: To find the translation vector, subtract the initial coordinates from the final coordinates for both x and y components.
Solution:
Identify the initial position P: (5, 7) and the final position P': (2, 4).
The x-component of the vector is the change in x-coordinates: x' - x. — a = 2 - 5 = -3
The y-component of the vector is the change in y-coordinates: y' - y. — b = 4 - 7 = -3
Combine these components to form the translation vector. — Vector = \(\begin{pmatrix} -3 \\ -3 \end{pmatrix}\)
8A rectangle has vertices P(1, 2), Q(4, 2), R(4, 0), and S(1, 0). If the rectangle is rotated 180° about the origin, what are the new coordinates of its vertex R'?
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Answer: (-4, 0)
Hint: For a 180° rotation about the origin, the rule is (x, y) → (-x, -y).
Solution:
Identify the coordinates of vertex R: (4, 0). — R = (x, y) = (4, 0)
Recall the rule for a 180° rotation about the origin: (x, y) → (-x, -y).
Apply the rule to point R. — R' = (-4, -0)
Simplify the coordinates. — R' = (-4, 0)
9Consider a triangle ABC. If it undergoes a translation to form triangle A'B'C', which of the following properties is guaranteed to be true?
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Answer: The area of triangle A'B'C' is equal to the area of triangle ABC.
Hint: Translations are 'rigid transformations', meaning they preserve certain properties of the original figure.
Solution:
Analyze Option A: Translation preserves orientation. So, A is false.
Analyze Option B: Translation is a rigid transformation, meaning it preserves lengths, and therefore perimeter. So, B is false.
Analyze Option C: Rigid transformations, including translation, preserve the size and shape of a figure, which means they preserve area. So, C is true.
Analyze Option D: Translation preserves side lengths. So, D is false.
10A point M' has coordinates (3, -5). It is the image of point M after a reflection in the line y = x. What were the original coordinates of point M?
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Answer: (-5, 3)
Hint: For a reflection in the line y = x, the x and y coordinates swap. To find the original point, apply the reverse of this rule.
Solution:
Identify the image coordinates M': (3, -5). — M' = (x', y') = (3, -5)
Recall the rule for reflection in the line y = x: (x, y) → (y, x).
To find the original point (x, y) from the image (y, x), simply swap the coordinates of M'. — M = (y', x') = (-5, 3)
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Tips for Transformations MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Transformations MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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