Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > High School Quizzes > Mathematics

Dilation Practice Quiz: Choose the Correct Answer

Explore transformation steps and key reasoning techniques

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting The Dilation Decision Challenge quiz for high school geometry students.

Which of the following best describes a dilation?
A transformation that changes the orientation of a figure
A transformation that enlarges or reduces a figure proportionally relative to a fixed center
A transformation that reflects a figure across an axis
A transformation that only rotates the figure
A dilation changes the size of a figure by scaling the distances from a fixed center point without altering the shape. It enlarges or reduces the figure proportionally, preserving the overall structure.
What is the effect of a dilation on the angles of a figure?
The angles become larger if the dilation is an enlargement
The angles are multiplied by the scale factor
The angles remain congruent
The angles become reversed
Dilation is a similarity transformation that preserves angle measures. Even though side lengths change, each angle remains congruent to its corresponding angle in the pre-image.
If a dilation has a scale factor of 1, what happens to the figure?
It becomes enlarged
It becomes reduced in size
It is reflected across the center
It remains unchanged
A scale factor of 1 means the distances from the center remain the same; therefore, every point maps to itself. The figure is congruent to its original position and size.
What is the center of dilation?
The vertex of the angle with the largest measure
A fixed point from which distances are measured and scaled
Any randomly selected point in the plane
The midpoint of one of the sides of the figure
The center of dilation is a specific, fixed point from which all distances to points in the figure are measured. It is used to uniformly scale the entire figure by the given factor.
Which equation correctly represents the image of a point P under a dilation with center O and scale factor k?
P' = k(P) - O
P' = P + k · O
P' = k · O + P
P' = O + k · (P - O)
The standard formula for a dilation with center O transforms point P to P' by scaling the vector from O to P by the factor k. This formula ensures that the dilation preserves the direction of the line through O and P.
When a figure undergoes a dilation with a scale factor greater than 1, what happens to the image?
The image is reflected
The image remains the same size
The image is enlarged
The image is reduced in size
A scale factor greater than 1 increases the distances from the center, thereby enlarging the figure proportionally. The shape remains similar to its original form, but its overall size increases.
If a dilation has a scale factor between 0 and 1, how does the image compare to the original?
The image is reduced in size
The image remains identical
The image is rotated
The image is enlarged
When the scale factor is between 0 and 1, each distance from the center is shortened, resulting in a smaller image. The figure stays similar, even though its size is decreased.
Which of the following properties is preserved under a dilation?
The area of the figure
The perimeter of the figure
The angle measures of the figure
The exact side lengths of the figure
Dilations preserve the shape of a figure, which means all angle measures remain the same. However, side lengths, perimeter, and area are scaled by the factor or its square, respectively.
Which of the following best explains why a dilation is considered a similarity transformation?
It merely shifts the figure without altering its size
It changes the shape and the angles of the figure
It reflects the figure without changing its overall dimensions
It preserves angles and maintains proportional relationships between side lengths
A dilation multiplies all distances by the same scale factor, preserving the ratios of corresponding side lengths and all the angle measures. This attribute means that the original and the image are similar in shape.
In a coordinate plane, if a point P(x, y) is dilated by a scale factor k with the origin as the center, what are the coordinates of the image P'?
P'(x/k, y/k)
P'(kx, ky)
P'(x + k, y + k)
P'(x, y) multiplied by (1 + k)
When a point is dilated from the origin, each coordinate is multiplied by the scale factor. This transformation scales the point radially outward or inward while preserving its direction from the origin.
A triangle undergoes a dilation with the center at one of its vertices. Which of the following remains unchanged?
The angle at the center of dilation remains unchanged
The length of the side opposite the center
The area of the triangle
The altitude from the center to the opposite side
The vertex that serves as the center of dilation stays fixed during the transformation, so its angle remains the same. Other attributes like side lengths and area are scaled according to the dilation factor.
If two figures are dilations of each other, which statement is true regarding their corresponding sides?
Their corresponding side lengths are equal
Their corresponding sides form congruent angles
There is no consistent relationship between their sides
Their corresponding side lengths are in proportion
Since a dilation scales every distance by the same constant factor, the ratios between all corresponding side lengths remain the same. This proportionality is the hallmark of similar figures.
What happens to the area of a figure when it undergoes a dilation with a scale factor k?
The area is multiplied by k²
The area is multiplied by k
The area is multiplied by 2k
The area remains unchanged
Dilations scale all linear dimensions by k; since area is a two-dimensional measurement, it scales by the square of the scale factor (k²). This quadratic relationship is a standard result in geometry.
Which step is necessary to determine the image of a figure under a dilation with a given center and scale factor?
Rotate the figure about the center by the scale factor
Translate each point by the value of the scale factor
Reflect each point across a specific axis through the center
Measure the distance from each point to the center, then multiply by the scale factor
To perform a dilation, you determine each point's distance from the fixed center and scale that distance by multiplying with the scale factor. This step-by-step process ensures all points map correctly relative to the center.
Given a dilation with center (2, 3) and a scale factor of 3, what is the image of the point (4, 5)?
(5, 4)
(6, 7)
(4, 5)
(8, 9)
Subtract the center (2, 3) from point (4, 5) to get (2, 2), scale this by 3 to obtain (6, 6), and then add back the center to reach (8, 9). This method follows the formula P' = O + k(P - O).
A line segment has endpoints A and B. Under a dilation with center A and scale factor k (k ≠1), what is the relationship between segment AB and the dilated image from A to B'?
B' lies on a line perpendicular to AB, unrelated to the original distance
B' lies on the ray AB, and the distance AB' is k times the original distance AB
B' lies on the ray BA, and the distance AB' is equal to AB
B' is reflected over point A, making AB' equal to half of AB
With A as the center of dilation, it remains fixed while point B is moved along the ray emanating from A through B. The distance from A to the image of B is exactly k times the original distance, reflecting the nature of the dilation.
Consider a circle undergoing a dilation with a scale factor of 2. How do the circumference and area of the circle change?
The circumference doubles and the area quadruples
Both the circumference and the area double
The circumference remains unchanged while the area quadruples
The circumference quadruples and the area doubles
A dilation scales one-dimensional measures like the circumference by the factor 2, while two-dimensional measures like the area are scaled by the square of the factor (2² = 4). This demonstrates the different scaling behaviors for length and area.
Which of the following statements is true for a dilation with a negative scale factor?
A negative scale factor rotates the figure by 90°
A negative scale factor produces a reflected and scaled image
Dilation cannot have a negative scale factor
A negative scale factor leaves the figure unchanged
While dilations typically use positive scale factors, a negative factor implies that the figure is not only scaled but also reflected across the center. This combined transformation results in a mirror image that is scaled accordingly.
If points A(1,2), B(3,4), and C(5,6) form a triangle, and a dilation with center (1,2) and a scale factor of 0.5 is applied, what happens to the triangle?
Vertex A remains fixed and vertices B and C move halfway toward A, shrinking the triangle
All vertices move away from the center, doubling the size of the triangle
The triangle is rotated 180° about point A
The triangle remains unchanged
Since the dilation center is at A, it remains in place while the other points move along the line joining them to A. With a scale factor of 0.5, the distances from A to B and A to C are halved, reducing the overall size of the triangle while preserving its shape.
A polygon undergoes a sequence of two dilations: first with center O and scale factor k, and then with the same center O and scale factor m. What is the overall effect on any point P of the polygon?
The overall effect is a rotation determined by the magnitudes of k and m
The overall effect is a translation combined with a dilation
The overall effect cannot be determined without additional coordinate information
The overall dilation is equivalent to a single dilation with scale factor k à - m and center O
When two dilations share the same center, their effects multiply. A point P is first scaled by k and then by m, resulting in an overall scale factor of k à - m with respect to the same center O.
0
{"name":"Which of the following best describes a dilation?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"Which of the following best describes a dilation?, What is the effect of a dilation on the angles of a figure?, If a dilation has a scale factor of 1, what happens to the figure?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Analyze the properties of dilation transformations in geometric figures.
  2. Identify corresponding points and distances in pre-image and image under dilation.
  3. Apply scale factors to compute new measurements after dilation.
  4. Evaluate the effects of different dilation centers on geometric shapes.
  5. Explain the relationship between proportional reasoning and dilation outcomes.

Dilation Quiz: Which Is a Dilation? Cheat Sheet

  1. Understanding Dilations - Think of dilations like your camera zoom feature! They resize shapes (keeping everything in perfect proportion) by using a center point and a scale factor, so you get an enlarged or shrunk version that's still similar to the original. When you dial up or down the size, the figures stay the same shape but get bigger or smaller. onlinemathlearning.com
  2. Center of Dilation - Imagine this as the "selfie spot" your shape stands on while you zoom in or out! All points move toward or away from this central point, determining where your new, rescaled figure lands. Changing the center shifts your entire image around the plane. Cuemath
  3. Scale Factor - Your magic number! A scale factor greater than 1 pumps up your figure to a larger size, while a value between 0 and 1 shrinks it down - perfect for creating mini versions. Adjusting this number is like turning the volume dial on your shape's size. Cuemath
  4. Properties Preserved Under Dilation - Dilations are shape-savers: angles stay the same and the resulting figures are always similar, like twins in different outfits. The only thing that changes is side length, which gets multiplied by the scale factor for that perfect size adjustment. It's like a photocopy trick that only changes size, never distorts features. onlinemathlearning.com
  5. Dilation on the Coordinate Plane - When you dilate a point (x, y) from the origin, you simply multiply both x and y by your scale factor k, landing you at (kx, ky) - math magic! This rule keeps things neat and predictable when you're working on a grid. Try it yourself and watch shapes expand or contract along straight rays from (0,0). Cuemath
  6. Negative Scale Factors - Throwing in a negative scale factor flips the figure like a pancake while resizing it - talk about multitasking! A factor like -2 not only doubles the size but also reflects the shape across the center of dilation. This nifty trick can create mirror images at different scales in one swoop. onlinemathlearning.com
  7. Identifying Scale Factor from Coordinates - Spot the pattern: divide your dilated point's coordinates by the original's, and voila, you've found the scale factor! For example, going from (3, 2) to (9, 6) screams a scale factor of 3. It's a quick calculation that turns coordinate puzzles into straightforward detective work. Dummies.com
  8. Effects on Line Segments - Lines that don't pass through the center stay perfectly parallel to their images, just longer or shorter by the scale factor. This means you can predict exactly how any segment's length will change, making geometry problems less mysterious. Wear your parallel-lines hat and watch the magic unfold! MathBitsNotebook.com
  9. Practice with Dilations - Drill time! Grab worksheets or online problems to dilate shapes with various centers and scale factors - muscle memory makes perfect. Hands-on practice helps you internalize how figures stretch, shrink, and move around the plane. For extra challenges, check out MathBitsNotebook's exercises! MathBitsNotebook.com
  10. Real-World Applications - From crafting scale models of buildings to reading maps, dilations are everywhere in real life. They help architects, engineers, and even video game designers maintain proportions while resizing objects. Understanding dilations gives you the superpower to interpret and create accurate scaled representations. Cuemath
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics Quizzes

Powered by: Quiz Maker