Questions and Answers
What transformation is represented by the rule (x, y)→(−x, −y)?
rotation of 180° about the origin
What transformation transforms (p, q) to (q, p)?
a reflection over y = x
Point (a, b) is transformed by the rule (a, b−4). What type of transformation occurred?
a translation of 4 units down
Point G(−7, 4) is translated using the rule (x+10, y−6). What is the x-coordinate of G′?
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Point H(9, 1) is reflected across the x-axis. Which statements about H′ are true? (Select each correct answer)
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What transformation is represented by the rule (x, y)→(y, −x)?
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What type of transformation transforms (a, b) to (−a, b)?
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Point (w, z) is transformed by the rule (w+5, z). What type of transformation occurred?
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Point B(6, −3) is translated using the rule (x−5, y+9). What is the y-coordinate of B′?
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Point T(3, −8) is reflected across the x-axis. Which statements about T′ are true? (Select each correct answer)
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What transformation is represented by the rule (x, y)→(−y, x)?
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What transformation transforms (a, b) to (a, −b)?
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Point (m, n) is transformed by the rule (m−3, n). What type of transformation occurred?
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Point P(−5, 2) is translated using the rule (x+3, y−1). What is the x-coordinate of P′?
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Point D(−1, 5) is reflected across the x-axis. Which statements about D′ are true? (Select each correct answer)
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Study Notes
Transformations and Their Rules
- The rule (x, y)→(−x, −y) represents a rotation of 180° about the origin.
- The transformation of (p, q) to (q, p) indicates a reflection over the line y = x.
- Transforming point (a, b) to (a, b−4) denotes a translation of 4 units downward.
- Point G(−7, 4) translated using (x+10, y−6) results in an x-coordinate of 3 for G′.
Reflections Across Axes
- Point H(9, 1) reflected across the x-axis yields H′ with an x-coordinate of 9 and a y-coordinate of −1.
- A transformation changing (a, b) to (−a, b) reflects the point over the y-axis.
- Point T(3, −8) reflected over the x-axis results in an x-coordinate of 3 and a y-coordinate of 8.
- A change from (a, b) to (a, −b) reflects the point over the x-axis.
- Point D(−1, 5) reflected over the x-axis produces an x-coordinate of −1 and a y-coordinate of −5.
Additional Transformations
- The rule (x, y)→(y, −x) signifies a rotation of 90° clockwise around the origin.
- The transformation (w, z) to (w+5, z) indicates a translation of 5 units to the right.
- Point B(6, −3) transformed using (x−5, y+9) results in a y-coordinate of 6 for B′.
- Transforming (m, n) to (m−3, n) shows a translation of 3 units to the left.
- The rule (x, y)→(−y, x) indicates a rotation of 90° counterclockwise around the origin.
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Description
Test your understanding of algebraic transformations in geometry with this quiz based on chapter 1.10. This quiz covers key concepts like reflections, translations, and rotations to solidify your grasp of how algebra describes geometric changes.
