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Quizzes > Mathematics

Transformations Unit Test: 20 Geometry Questions to Check Your Skills

Quick geometry transformations quiz: 20 questions, instant results, targeted review tips.

Editorial: Review CompletedCreated By: Aatish MotiparaUpdated Aug 24, 2025
Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art promoting a high school geometry quiz on transformations

This transformations unit test helps you practice translations, reflections, rotations, and dilations on the coordinate plane. Work through 20 quick questions for instant results and clear next steps to review. For more practice, try a geometry review quiz, a geometry quiz with answers, or build basics with a geometry unit 1 test.

Which transformation maps point (3, -2) to (3, 5)?
Translation by vector <0, 7>
Reflection across the x-axis
Rotation 90 degrees counterclockwise about the origin
Translation by vector <7, 0>
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Reflect point (-4, 2) across the y-axis. What is the image?
(4, 2)
(-2, 4)
(-4, -2)
(2, -4)
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A dilation centered at the origin with scale factor 2 maps (x, y) to which rule?
(x+2, y+2)
(x/2, y/2)
(2x, y/2)
(2x, 2y)
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Which transformation preserves both distance and angle measure?
Translation
Non-uniform scaling
Horizontal stretch by factor 2
Dilation with scale factor 3
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Which coordinate rule represents a reflection across the line y = x?
(x, y) -> (y, x)
(x, y) -> (-y, -x)
(x, y) -> (x, -y)
(x, y) -> (-x, y)
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What is the translation vector that maps P( -3, 4 ) to P'(2, -1)?
<5, 1>
<5, -5>
<-5, -5>
<2, 1>
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A rotation of 180 degrees about the origin maps (a, b) to which ordered pair?
(a, -b)
(b, -a)
(-b, a)
(-a, -b)
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Under a 90-degree counterclockwise rotation about the origin, where does (1, -5) map?
(-1, 5)
(-5, -1)
(1, 5)
(5, 1)
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Which term describes a composition of a reflection followed by a translation along the mirror line?
Glide reflection
Shear
Dilation
Rotation
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The image of triangle ABC after a transformation is A'B'C'. Which statement guarantees the transformation is an isometry?
Only AB = A'B'
Area of A'B'C' is four times area of ABC
Perimeter of A'B'C' is twice the perimeter of ABC
AB = A'B', BC = B'C', and CA = C'A'
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Which statement about orientation is true for a single reflection in the plane?
A reflection preserves orientation
A reflection reverses orientation
Orientation depends on segment lengths only
Orientation is undefined after a reflection
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A dilation centered at (0, 0) with scale factor 1/2 changes the area of a polygon by what factor?
4
2
1/2
1/4
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Under reflection across y = -x, where does the point (7, -2) map?
(-2, 7)
(2, -7)
(7, 2)
(-7, 2)
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Which line is the perpendicular bisector of the segment connecting (3, 1) and (5, 3)?
y = -x + 7
x - y = 0
y = x + 1
x + y = 6
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Under dilation centered at the origin with k = -2, where does (3, -1) map?
(-3, 1)
(1.5, -0.5)
(-6, 2)
(6, -2)
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Which equation is the line of reflection that maps (4, 1) to (-2, 1)?
x = -1
y = -1
y = 1
x = 1
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A dilation centered at (2, -1) with k = 2 maps point (4, 3) to which point?
(8, 6)
(6, 7)
(0, -5)
(2, -1)
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Under a 270-degree clockwise rotation about the origin, (x, y) maps to:
(x, y)
(-y, x)
(y, -x)
(-x, -y)
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A tessellation by regular hexagons is possible because hexagons have interior angle measure of:
100 degrees, which fits 3 at a point (3*100 = 300)
90 degrees, which fits 4 at a point (4*90 = 360)
120 degrees, which fits 3 at a point (3*120 = 360)
150 degrees, which fits 2 at a point (2*150 = 360)
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Every rigid motion in the plane can be expressed as a composition of which transformations?
Reflections
Non-uniform scalings
Dilations
Shears
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0

Study Outcomes

  1. Understand the characteristics and properties of translations, rotations, and reflections.
  2. Apply transformation rules to manipulate geometric figures.
  3. Analyze the impact of each transformation on the position and orientation of shapes.
  4. Evaluate transformation results using coordinate and visual methods.

Transformations Unit Test Review Cheat Sheet

  1. Understand the Four Main Types of Transformations - Get cozy with translations (slides), rotations (turns), reflections (flips), and dilations (resizing). Each shape‑shifting trick moves or resizes figures in a unique way, giving you a toolbox of moves to master. Practice visualizing how each one affects a figure's position and size to level up your geometry game.
  2. Master Translation Rules - Learn to slide figures horizontally and vertically on the coordinate plane without rotating or resizing them. For example, moving point (x, y) 3 units right and 2 units up turns it into (x + 3, y + 2). Nail these rules and you'll see every shape glide perfectly where you want it.
  3. Grasp Reflection Concepts - Flip shapes over the x-axis, y-axis or any mirror line and watch coordinates change sign. Reflecting (x, y) over the x-axis creates (x, - y), while the y-axis flip makes it ( - x, y). Understanding these mirror moves will sharpen your symmetry skills in no time.
  4. Comprehend Rotation Mechanics - Spin figures around a point by specific degrees to see them land in new positions. A 90° counterclockwise turn around the origin sends (x, y) to ( - y, x). Mastering these moves lets you rotate shapes confidently and visualize every twist.
  5. Explore Dilation and Scale Factors - Resize shapes by multiplying coordinates by a scale factor. Apply a factor of 2 to point (x, y) and it becomes (2x, 2y), making the shape twice as large. Play with different factors to see how figures grow and shrink!
  6. Practice Composition of Transformations - Combine moves, like reflecting a shape then sliding it, to see how sequences stack. For example, flip a triangle over the x-axis, then translate it up 3 units to land in a brand‑new spot. These combo moves are key to tackling complex problems step by step.
  7. Identify Symmetry in Figures - Spot line and rotational symmetry in shapes to predict how they'll look after transformations. A square, for instance, has four lines of symmetry and rotates onto itself every 90°. Recognizing these patterns unlocks shortcuts in proofs and constructions.
  8. Apply Transformations to Graphs - Shift, stretch or reflect graphs of functions to see their new equations at a glance. Translating y = x² two units up flips it to y = x² + 2, while reflecting over the x-axis gives you y = - x². Practicing these tweaks makes graphing fast and fun.
  9. Understand Rigid vs. Non‑Rigid Transformations - Rigid transformations (translations, rotations, reflections) preserve size and shape, while non‑rigid ones (dilations) change scale. Knowing which moves keep measurements intact helps you decide the right tool for proofs and problem solving.
  10. Utilize Online Resources for Practice - Reinforce your transformation skills with interactive quizzes, flashcards, and hands‑on activities. Regular practice builds confidence and makes these concepts second nature, so you can tackle any geometry challenge.
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