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11 multiple-choice questions and 11 flashcards on Transformations and Symmetry, about 7% of the High School Geometry bank. Every one carries a written rationale.
Transformations and Symmetry is one of 13 chapters in CoStudy's High School Geometry bank, and it holds 11 of the bank's 150 multiple-choice questions — roughly 7% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
9 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
A rigid motion (translation, rotation, or reflection):
Answer: A — Preserves distance and angle measure
A) Rigid motions (isometries) preserve BOTH distance and angle measure — that's the definition. B) False — angles are preserved. C) False — area is preserved precisely because distances are. D) Describes a dilation (similarity), not a rigid motion.
The point (−4, 6) is reflected across the line y = x. Its image is:
Answer: C — (6, −4)
A) Rotation 180° about origin. B) Reflection across y-axis. C) Reflection across y = x swaps coordinates: (a, b) → (b, a), so (−4, 6) → (6, −4). D) Negated and swapped.
Which transformation preserves both ORIENTATION and SIZE?
Answer: E — Translation (slides without flipping or resizing)
Rigid transformations preserve size: translation, rotation, reflection. Translation and rotation also preserve orientation. Reflection reverses orientation. Dilation changes size (similarity transformation). Translation is the most direct answer.
Which transformation does NOT preserve distance?
Answer: D — Dilation (scale factor ≠ 1)
A/B/C) All three are rigid motions (isometries) — distance is preserved. D) A dilation with scale factor ≠ 1 changes lengths by that factor; only angles are preserved.
A translation of (x, y) → (x + 4, y − 2) followed by another (x, y) → (x − 1, y + 5) is equivalent to:
Answer: D — (x + 3, y + 3)
D) Composition of translations adds vectors: (+4, −2) + (−1, +5) = (+3, +3). B) Added absolute values. C) Subtracted everything. A) Only the first translation.
Area of a sector with radius 6 and central angle 60°:
Answer: C — 6π (Area = (θ/360°)·πr² = (60/360)·π·36 = (1/6)·36π = 6π)
Sector area: (θ/360°)·πr² for degree θ. (60/360)·π·36 = (1/6)(36π) = 6π. Arc length similarly: (θ/360°)·2πr. Radians simplify: A = (1/2)r²θ.
A dilation centered at the origin with scale factor 1/2 maps the segment from (4, 8) to (8, 12) to a segment of length:
Answer: A — 1/2 × √32
A) Original length = √((8−4)² + (12−8)²) = √32. Dilation by 1/2 multiplies LENGTHS by 1/2, so the new length is (1/2)√32. B) Forgot to apply the dilation. C) Used scale factor 2 instead of 1/2. D) Squared the factor by mistake.
Reflecting the point (4, −3) across the y-axis produces:
Answer: D — (−4, −3)
A) Reflection across the x-axis. B) Reflection across both axes (rotation 180° about origin). C) Rotation 90° counterclockwise about origin. D) Reflection across the y-axis maps (x, y) → (−x, y), so (4, −3) → (−4, −3).
Two triangles have side ratios 2:5. If smaller has area 12, larger has area:
Answer: B — 75 (area scales as square of linear scale; (5/2)² = 25/4; 12 × 25/4 = 75)
Similar figures: area ratio = (linear ratio)². If linear ratio 2:5, area ratio 4:25. Larger area = 12 · (25/4) = 75. Volume scales as cube of linear ratio.
4 cards from the 11 in this chapter.
Reflect (4, 7) across the x-axis. Result?
(4, −7).
Rotate (3, 4) 180° about origin. Result?
(−3, −4). Rule: (x, y) → (−x, −y).
What is a 'dilation'?
Resizing a figure by a scale factor (with respect to a center).
What is a 'reflection'?
Flipping a figure across a line of reflection (mirror image).
These are a sample. The full Transformations and Symmetry chapter runs 22 items with per-chapter progress tracking, on the web and in the iOS app.
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