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Quizzes > High School Quizzes > Mathematics

Transformations Unit Practice Quiz

Review key transformation concepts with our test

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art promoting a high school geometry quiz on transformations

Easy
What is a translation in geometry?
A reflection over a line
A rotation about a central point
A slide move that shifts figures horizontally, vertically, or both without rotation
A resizing of a shape that changes its size
Translation moves every point of a shape a constant distance in a specific direction. It does not change the size, shape, or orientation of the figure.
Which of the following is true about rotations?
It enlarges a figure by a scale factor
It slides a figure in a parallel direction
It flips a figure over a line
It turns a figure about a fixed point where every point moves along an arc
A rotation turns a figure about a fixed point while moving every point along a circular arc. This transformation preserves both the size and shape of the figure.
Which transformation results in a mirror image of a figure?
Reflection
Translation
Rotation
Dilation
Reflection flips a figure over a line to produce a mirror image. It preserves the size and shape while reversing the orientation.
In a reflection, what is the role of the line of reflection?
It is the center point about which the figure rotates
It is the fixed line where each point and its image are equidistant
It determines the scale factor for resizing
It is the path along which every point moves
The line of reflection is like a mirror that every point in the shape is equidistant from. It ensures that the reflected image is congruent to the original figure.
Which property is preserved under all rigid transformations (translations, rotations, and reflections)?
Orientation only
Size and shape
Distance only
Area only
Rigid transformations preserve the size and shape of figures. They maintain the distances and angles, ensuring that the original figure and its image are congruent.
Medium
What is the effect of a translation on the coordinates of a point (x, y)?
They rotate around the origin
They become (ax, by)
They reflect across the line y = x
They become (x + a, y + b) when translated by a and b
A translation adds constant values to the x and y coordinates of a point. This operation shifts the point without changing its orientation or size.
Which of these transformations is not an isometry?
Translation
Reflection
Rotation
Dilation
Isometries preserve distances and angles, keeping the original shape and size intact. Dilation, however, changes the size of a figure, making it the non-isometric transformation among the options.
A rotation of 90° counterclockwise about the origin sends the point (2, 3) to which of the following?
(-2, -3)
(-3, 2)
(3, -2)
(2, 3)
Rotating a point (x, y) 90° counterclockwise about the origin transforms it to (-y, x). Applying this rule to (2, 3) results in (-3, 2).
If a shape is first rotated 180° about the origin and then reflected over the y-axis, the final position of the shape results in what transformation overall?
Translation
Rotation of 180°
Reflection over the x-axis
Reflection over the y-axis
Rotating a shape 180° sends (x, y) to (-x, -y), and reflecting that over the y-axis then sends (-x, -y) to (x, -y). The resulting transformation is equivalent to a reflection over the x-axis.
What is the result of applying a reflection to a shape with respect to a line not intersecting the shape?
The shape is rotated around the line
The shape changes its orientation but not its position
The shape is flipped to the opposite side of the line maintaining congruency
The shape is enlarged
When a shape is reflected across a line, it is flipped to the opposite side while remaining congruent to the original shape. The distance from the reflecting line remains the same for corresponding points.
Which transformation can be used to prove two triangles are congruent by overlaying one onto the other?
Shearing
Scaling
Combination of translations, rotations, and reflections
Dilation
Rigid motions, which include translations, rotations, and reflections, preserve the size and shape of figures. Using a combination of these transformations can overlay one triangle perfectly onto another to prove congruence.
How does a rotation affect the orientation of a shape?
It always reverses the orientation
It preserves the orientation even if rotated 180°
It enlarges the shape
It changes the orientation unless the rotation is 0° or 360°
A rotation alters the angle at which a shape is positioned. Except for a full rotation (0° or 360°), the orientation is visibly changed, although the size and shape remain constant.
What is the primary reason why dilations are not considered rigid motions?
Because they change the position of the figure
Because they flip the figure
Because they rotate the figure
Because they do not preserve the size of the figure
Dilations change the overall size of a figure by scaling the distances between points. While they preserve the shape (angle measures remain the same), the size alteration means they are not rigid motions.
After a 270° clockwise rotation, what is the image of point (4, 1) about the origin?
(4, 1)
(-1, 4)
(-4, -1)
(1, -4)
A 270° clockwise rotation corresponds to a 90° counterclockwise rotation. By using the rotation rule (x, y) → (-y, x), the point (4, 1) is transformed to (-1, 4).
Which transformation requires a point (the center) to determine how far and in what direction every other point moves?
Rotation
Translation
Reflection
Dilation
Rotation involves turning a figure about a fixed point known as the center of rotation. Each point in the figure moves in an arc around this center, which defines both the direction and the distance of the movement.
Hard
A composite transformation consists of a reflection across the line y = x followed by a rotation of 90° counterclockwise about the origin. What is the image of the point (3, -1) under this composite transformation?
(-1, -3)
(1, 3)
(3, 1)
(-3, -1)
Reflecting (3, -1) across the line y = x swaps the coordinates, resulting in (-1, 3). Then, rotating (-1, 3) 90° counterclockwise using the rule (x, y) → (-y, x) gives (-3, -1).
If a dilation centered at the origin with a scale factor of 2 is applied to a circle with radius r, how does the area of the circle change?
The area becomes 4 times larger
The area becomes 2 times larger
The area remains the same
The area doubles
When a figure is dilated, linear dimensions are multiplied by the scale factor and areas are multiplied by the square of that factor. With a scale factor of 2, the area increases by 2², or 4 times.
Consider a transformation matrix representing a rotation about the origin. Which matrix corresponds to a 90° counterclockwise rotation?
[[0, -1], [1, 0]]
[[0, 1], [-1, 0]]
[[1, 0], [0, 1]]
[[-1, 0], [0, -1]]
The standard rotation matrix for a 90° counterclockwise rotation is [[0, -1], [1, 0]], which converts the point (x, y) to (-y, x). This matrix uniquely represents the 90° counterclockwise rotation.
A shape undergoes a rotation followed by a dilation with a scale factor of 1. Which property changes as a result of the composite transformation?
The side lengths are doubled
No property changes
The size (area) of the shape increases
The orientation of the shape changes
A dilation with a scale factor of 1 leaves the size of a shape unchanged, acting as the identity transformation. However, the preceding rotation alters the orientation of the shape while keeping its dimensions and area intact.
When two reflections are composed over intersecting lines, what is the resulting transformation?
Reflection
Translation
Rotation about the point of intersection
Dilation
Reflecting over two intersecting lines results in a rotation, where the angle of rotation is twice the angle between the reflecting lines. The center of rotation is the intersection point of the two lines.
0
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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. Dive into transformations
  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. Translation guide
  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. Reflection practice
  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. Rotation walkthrough
  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! Scale up with dilations
  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. Mix and match moves
  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. Symmetry secrets
  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. Graph transformations
  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. Rigid vs non‑rigid breakdown
  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. Practice flashcards
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