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Quizzes > High School Quizzes > Mathematics

Dilation Practice Quiz: Ace Your Exam

Sharpen Your Skills with Effective Practice Worksheets

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Dilation Dynamics Quiz for high school geometry students.

Which transformation produces an image that is the same shape but a different size?
Reflection
Rotation
Dilation
Translation
A dilation changes the size of an object while keeping its shape consistent. The other transformations do not alter the size in such a manner.
How does a dilation with a scale factor less than 1 affect a figure?
It enlarges the figure
It reflects the figure
It shrinks the figure
It rotates the figure
A scale factor less than 1 reduces the size of the figure, producing a smaller image while maintaining its shape. The other options do not correctly describe this effect.
What is the center of dilation?
The midpoint of a segment
The fixed point from which all points are stretched or shrunk
The farthest point from the object
The angle bisector
The center of dilation is the point that remains unchanged and serves as a fixed reference while other points scale relative to it. The other choices do not represent the correct concept.
In a dilation, what remains unchanged after the transformation?
The figure's area
The coordinates of every point
The length of each side
The ratio of corresponding side lengths
A dilation preserves the ratios of corresponding side lengths, ensuring the image is similar to the original. However, individual lengths, area, and specific coordinates are modified by the scale factor.
If a dilation produces an image with coordinates (4, 8) from a preimage point (2, 4), what is the scale factor?
8
2
4
0.5
Multiplying the preimage coordinates (2, 4) by 2 yields the image coordinates (4, 8). Thus, the scale factor used in the dilation is 2.
Which coordinate transformation represents a dilation with a scale factor of 3 centered at the origin?
(x, y) -> (x+3, y+3)
(x, y) -> (3x, 3y)
(x, y) -> (x/3, y/3)
(x, y) -> (3x, y)
Multiplying both the x and y coordinates by 3 scales the figure uniformly from the origin. The other options do not reflect a uniform dilation centered at the origin.
If a point (a, b) undergoes a dilation centered at (0, 0) with scale factor k, what are its image coordinates?
(a/k, b/k)
(ka, kb)
(a + k, b + k)
(a - k, b - k)
A dilation centered at the origin multiplies each coordinate by the scale factor k, resulting in (ka, kb). Other options mistakenly add, divide, or subtract the scale factor.
In a dilation centered at a point other than the origin, which method correctly computes the image of a point?
Reflect across the center then apply the scale factor
Add the scale factor to each coordinate
Translate so that the center is at the origin, apply dilation, then translate back
Multiply the coordinates directly by the scale factor
When the center is not at the origin, the correct approach is to translate the point so that the center becomes the origin, perform the dilation, and then translate back. This ensures accuracy in the computed image.
Which dilation scale factor reduces the area of a figure to one-quarter of its original size?
1/2
4
2
1/4
The area after dilation scales by the square of the scale factor. A scale factor of 1/2 results in an area of (1/2)², which is 1/4 of the original area.
A triangle with vertices at (1,2), (3,4), and (5,6) is dilated about the origin by a factor of 3. What is the image of the vertex (3,4)?
(6,8)
(3,4)
(4,3)
(9,12)
Multiplying each coordinate of (3,4) by 3 yields the image (9,12). This is the standard method for performing a dilation centered at the origin.
Which property of a figure is preserved after a dilation?
Coordinate values
Area
Exact side lengths
All angle measures
A dilation preserves angle measures, ensuring that the resulting figure is similar to the original. Although side lengths, area, and coordinates are altered by the scale factor, the angles remain unchanged.
If the scale factor of a dilation is 5, by what factor are distances from the center multiplied?
1/5
5
0
25
The scale factor directly multiplies the distance of every point from the center of dilation. Thus, a scale factor of 5 means each distance is multiplied by 5.
When a dilation is applied to a line segment with endpoints (2,3) and (4,7) using a scale factor of 2 centered at the origin, what is the relationship between the original length L and the new length?
The new length remains L
The new length is 2L
The new length is L/2
The new length is 4L
Dilation with a scale factor multiplies all distances by that factor. Consequently, the length of the segment becomes 2 times L when a factor of 2 is applied.
Consider a rectangle with a length of 8 and a width of 3. If it undergoes a dilation with a scale factor of 1/2, what is the new area?
8
6
12
24
The original area is 8 x 3 = 24. Under dilation, the area scales by the square of the scale factor: (1/2)² x 24 = 6.
What is the effect of a dilation with a negative scale factor on a figure?
It produces a reflection combined with scaling
It only scales the figure without reflecting it
It rotates the figure
It only reflects the figure without scaling
A negative scale factor indicates that the figure is both scaled and reflected through the center of dilation. This means the orientation is reversed along with the scaling.
Given a dilation centered at (2, -1) with scale factor k, if the point (4, 3) maps to (6, 7), what is k?
3
1
2
4
Using the dilation formula, the image is computed as: image = center + k × (original point - center). Substituting the values, both the x and y equations yield k = 2.
A dilation centered at (h, k) sends point A to A' and point B to B'. If the distance between A and B is 10 and the distance between A' and B' is 30, what is the scale factor?
10
1/3
30
3
The scale factor of a dilation is determined by the ratio of any two corresponding distances. Here, 30 divided by 10 gives a scale factor of 3.
Two similar figures are related by a dilation with scale factor k. If the perimeter of the original figure is P, what is the perimeter of the dilated image?
P + k
P/k
k²P
kP
Under a dilation, all linear dimensions, including the perimeter, are multiplied by the scale factor k. Therefore, the dilated perimeter is k times P.
If a scale factor of 0.75 is applied to a figure, which of the following statements accurately describes the change in area and perimeter?
Both the perimeter and area are 0.75 times the original
The perimeter is 0.75 times the original and the area is 0.5625 times the original
The perimeter remains the same and the area is 0.75 times the original
The perimeter is 0.5625 times the original and the area is 0.75 times the original
The perimeter of a figure scales directly with the scale factor (0.75), while the area scales by the square of the scale factor (0.75² = 0.5625).
A polygon undergoes two consecutive dilations: first by a scale factor of 2 and then by a scale factor of 0.5, both centered at the origin. What is the overall effect on the polygon?
The polygon remains unchanged in size
The polygon flips orientation
The polygon is enlarged by a factor of 1
The polygon is shrunk by a factor of 1
The overall effect of consecutive dilations is the product of the individual scale factors. Here, 2 × 0.5 equals 1, so the polygon's size remains the same.
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Study Outcomes

  1. Analyze the properties of dilations and their effects on geometric figures.
  2. Apply scale factors to accurately transform coordinates and dimensions.
  3. Determine corresponding sides and angles between original and dilated figures.
  4. Solve problems that require computation of dilation factors in various scenarios.
  5. Evaluate the impact of dilations on the overall shape and size of figures.

Dilation Practice Cheat Sheet

  1. Understanding Dilations - Think of dilation as the ultimate copy-paste tool that scales a shape up or down while keeping it looking identical. The center of dilation is your "anchor" point that everything stretches or shrinks away from. Dilation Transformation
    2. Dilation Transformation
  2. Scale Factor Basics - The scale factor tells you the "zoom level" of your dilation: values above 1 blow your figure up, while values between 0 and 1 shrink it. It's super handy for predicting exactly how big or small your new shape will be. Dilation Geometry
    3. Dilation Geometry
  3. Calculating Scale Factor - Just divide any side length in the image by the matching original side length to get your scale factor. For example, if the original is 4 units and the copy is 8, bam - you've got a scale factor of 2! Dilation Practice
    4. Dilation Practice
  4. Dilations on the Coordinate Plane - When you dilate on an (x, y) grid, simply multiply each coordinate by your scale factor: (x, y) → (kx, ky). This trick gives you a quick way to graph your scaled figure without breaking a sweat. Geometry Dilation
    5. Geometry Dilation
  5. Properties Preserved Under Dilations - Dilations keep every angle intact and all sides proportional, so your larger or smaller shape still "feels" the same. Just remember: while shape stays true, actual distance and area will change according to the scale factor. Dilations & Lines Practice
    6. Dilations & Lines Practice
  6. Negative Scale Factors - A negative scale factor not only resizes your figure but also flips it like a pancake across the center of dilation. It's a two‑in‑one move: reflection plus scaling! Dilation Transformation
    7. Dilation Transformation
  7. Center of Dilation - This is the "home base" from which everything radiates or contracts. If it's at the origin (0, 0), your calculations are a breeze; if it's elsewhere, you'll need a quick shift before scaling. Center of Dilation
    8. Center of Dilation
  8. Identifying Scale Factor from Coordinates - Spot the original and image points, then divide their coordinates to find k. For example, mapping A(3, 2) to A′(9, 6) gives you 9/3 = 3. Easy practice for coordinate champs! Dilation Scaling Practice
    9. Dilation Scaling Practice
  9. Effects of Scale Factor on Area - While lengths scale by k, areas explode by k² - so doubling a shape makes it four times bigger in area. This powerful insight helps you predict area changes instantly. Geometry Dilation
    10. Geometry Dilation
  10. Practice with Grid Dilations - Grab some graph paper (or an online grid) and play with different centers and scale factors. These hands‑on exercises make those abstract rules stick like glue! Grid Dilations Practice
    11. Grid Dilations Practice
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