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

Practice Quiz: Unit 2 Dilations & Similarity Answers

Master dilations and similarity with guided solutions

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Colorful paper art promoting The Scale and Similarity Challenge high school geometry quiz

Which of the following best defines a dilation transformation?
A transformation that reflects a figure across a line.
A transformation that translates a figure without altering its size.
A transformation that rotates a figure around a fixed point.
A transformation that scales a figure either larger or smaller while preserving its shape.
A dilation changes the size of a figure by a constant scale factor while maintaining its shape and proportions. It does not affect the angles or alter the overall structure of the figure.
What is the scale factor in a dilation?
The number of degrees a figure is rotated.
The fixed point used during the transformation.
The ratio of the length of any side of the image to the corresponding side of the original.
The distance a figure is translated.
The scale factor is defined as the ratio of any corresponding linear measurement in the image to that of the pre-image. It indicates how much larger or smaller the image is compared to the original figure.
If two figures are similar, what can be said about their corresponding angles?
They are supplementary.
They vary depending on the scale factor.
They are complementary.
They are congruent.
Similar figures have corresponding angles that are congruent, meaning they have equal measures. This property is essential for maintaining the shape of the figure during scaling.
Which of the following is a property of dilations?
They primarily rotate a figure around a fixed point.
They preserve the shape of a figure while changing its size.
They preserve the size of a figure but change its shape.
They reflect a figure over a line.
Dilations enlarge or reduce figures by a constant scale factor, ensuring that the shape remains unchanged. Only the size is affected and the proportional relationships between sides and angles are maintained.
In a dilation transformation, which point remains fixed?
All vertices remain fixed.
The center of dilation remains fixed.
The centroid remains fixed.
The midpoint of every side remains fixed.
The center of dilation is the invariant point in a dilation transformation; it does not move while all other points are repositioned relative to it. This point serves as the reference for scaling the entire figure.
Given a triangle with vertices (1,2), (3,2), and (1,4), if a dilation centered at (0,0) with a scale factor of 2 is applied, what is the new coordinate of point (3,2)?
(2,1)
(0,0)
(3,4)
(6,4)
Dilation from the origin involves multiplying each coordinate by the scale factor. Thus, (3,2) becomes (3×2, 2×2) = (6,4).
Two similar triangles have a scale factor of 3:1. If a side in the smaller triangle measures 4 units, what is the length of the corresponding side in the larger triangle?
12 units
1.33 units
9 units
7 units
A scale factor of 3:1 indicates that each side of the larger triangle is three times as long as its corresponding side in the smaller triangle. Therefore, 4 units becomes 4×3 = 12 units.
If two similar figures have a scale factor of 1:4, what is the ratio of their areas?
4:1
1:4
1:8
1:16
The area of similar figures scales by the square of the scale factor. Since (1:4) squared is (1²:4²) = 1:16, the areas are in the ratio 1:16.
If triangle ABC is similar to triangle DEF and the length of side AB is 8 while the corresponding side DE is 4, what is the scale factor from triangle ABC to triangle DEF?
0.5
4
2
1.5
The scale factor is determined by dividing the side of the image by the side of the pre-image. Here, 4 divided by 8 is 0.5, indicating that triangle DEF is half the size of triangle ABC.
Given two similar rectangles where the smaller has dimensions 3 by 5, and the larger is a dilation with a scale factor of 2, what is the area of the larger rectangle?
30
15
60
45
The area of the smaller rectangle is 3×5 = 15. With a dilation scale factor of 2, the area increases by the square of the scale factor: 15×(2²) = 15×4 = 60.
Which of the following is a valid criterion for triangle similarity?
Only one pair of congruent sides
Equal perimeters
Two pairs of congruent angles
Equal areas
Triangles are similar if they have two pairs of congruent angles (AA similarity). This guarantees that the third pair of angles is also congruent, maintaining proportionality between corresponding sides.
A dilation sends a point (x, y) to (3x, 3y). What is the scale factor of this dilation?
x + y
6
3
1/3
Since both x and y coordinates are multiplied by 3, the scale factor of the dilation is 3. This means every distance from the origin is tripled.
A line segment with endpoints (2, -1) and (2, 3) is dilated from the point (2, -1) with a scale factor of 4. What is the new coordinate of the endpoint originally at (2, 3)?
(2,15)
(6,11)
(2,-3)
(2,7)
The dilation is centered at (2, -1), which stays fixed. The vector from the center to (2,3) is (0,4); multiplying this by 4 gives (0,16), which when added back to the center yields (2,15).
When a polygon is enlarged by a scale factor of 3, by what factor does its perimeter increase?
None, the perimeter remains the same
3
6
9
In a dilation, linear measurements such as the perimeter are directly multiplied by the scale factor. Thus, a polygon enlarged by a factor of 3 will have a perimeter that is three times as long.
In any dilation, which property of the original figure is preserved?
Area
Angle measures
Side lengths
Absolute coordinates
Dilations preserve the shape of the figure, meaning that all angle measures remain the same. Although the side lengths and area change, the proportional relationships between all parts are maintained.
If the areas of two similar triangles are in the ratio 9:16, what is the linear scale factor from the smaller triangle to the larger triangle?
9/16
16/9
4/3
3/4
The area ratio of similar figures is the square of the linear scale factor. Taking the square root of 16/9 gives 4/3, which is the scale factor from the smaller to the larger triangle.
Triangle ABC is similar to triangle DEF. If the sides of triangle ABC are 5, 12, and 13, and the longest side of triangle DEF is 26, what is the scale factor from ABC to DEF?
3
2
0.5
1.5
The longest side of triangle ABC is 13, and its corresponding side in triangle DEF is 26. Dividing 26 by 13 gives a scale factor of 2.
A dilation with center (3, -2) maps point (7,4) to (11,10). What is the scale factor of this dilation?
2
1/2
4
3
Using the dilation formula: (11,10) = (3,-2) + k×((7-3), (4-(-2))) = (3,-2) + k×(4,6). Solving 3 + 4k = 11 gives k = 2, which is confirmed by the y-coordinate calculation.
A parallelogram with vertices at (1,2), (4,2), (4,5), and (1,5) is dilated from the point (1,2) with a scale factor of 3. What is the area of the dilated parallelogram?
27
81
63
45
The original parallelogram is a rectangle with width 3 and height 3, giving an area of 9. Under dilation, the area scales by the square of the scale factor (3² = 9), so the new area is 9×9 = 81.
In similar figures, if the perimeters are in the ratio 3:5 and the shortest side of the smaller figure is 6 units, what is the corresponding side length of the larger figure?
9
12
10
8
The ratio of corresponding side lengths in similar figures matches the ratio of their perimeters. Multiplying the shorter side 6 units by (5/3) yields 10 units for the larger figure.
0
{"name":"Which of the following best defines a dilation transformation?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"Which of the following best defines a dilation transformation?, What is the scale factor in a dilation?, If two figures are similar, what can be said about their corresponding angles?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Understand the concept of scale factors in similar figures.
  2. Apply dilation rules to transform geometric shapes accurately.
  3. Analyze the effects of scaling on dimensions and proportions.
  4. Evaluate the criteria for similarity in geometric figures.
  5. Solve complex problems involving transformations and similar figures.

Practice Quiz 7 Unit 2: Dilations & Similarity Answers Cheat Sheet

  1. Similarity Basics - Similar figures share shape but can be different sizes; their corresponding angles match like puzzle pieces and sides stretch up or shrink down in perfect proportion. Getting this concept down is like discovering your math superpower for figuring out mysterious shapes. Dilations and Similarity - MathBitsNotebook(JR)
  2. Dilations Unleashed - Dilations resize a figure from a center point using a scale factor, so your shape grows or shrinks while keeping its angle personality intact. It's like zooming in or out on a photo without blurring the picture! Generating Similar Figures Using Dilations | Texas Gateway
  3. Scale Factors - If your scale factor is greater than 1, your figure gets a makeover and enlarges; between 0 and 1, it shrinks down for a sleek mini version. Choosing the right factor is crucial for controlling your shape's size - no drama, just math magic. Generating Similar Figures Using Dilations | Texas Gateway
  4. Corresponding Sides & Angles - Identifying which sides and angles line up is your ticket to solving proportional puzzles in similar figures. Once you've paired them up, set up a proportion, solve it, and watch your confidence in geometry soar! Generalizing Proportions from Similar Figures | Texas Gateway
  5. Coordinate Plane Dilations - When dilating in the coordinate plane, every point (x,y) moves away from or toward the center by multiplying the coordinates by the scale factor. Knowing how coordinates transform makes plotting easier than ever - not to mention super satisfying. Generating Similar Figures Using Dilations | Texas Gateway
  6. Similarity Transformations - Similarity transformations combine translations, rotations, reflections, and dilations to map one figure onto another without losing shape. Mixing and matching these moves is like choreographing a dance for your shapes - fun and powerful! Illustrative Mathematics - Students | IM Demo
  7. Triangle Similarity Criteria - Use AA, SAS, or SSS to check if two triangles are long-lost twins in disguise; matching two angles or fitting sides in proportion reveals the secret. Mastering these shortcuts makes triangle comparisons a breeze. Similarity Outline - MathBitsNotebook (Geo)
  8. Perimeters & Areas - When figures are similar, their perimeters scale by the factor itself, but their areas go by the square of that factor - double the factor, quadruple the area! Armed with this rule, you can tackle real-world design and architecture problems with ease. Illustrative Mathematics - Students | IM Demo
  9. Parallel Lines & Dilations - Dilations send most lines off to parallel paths unless they pass through the center, in which case they stay put. This trick is essential for analyzing geometric figures after a dilation has worked its magic. Generating Similar Figures Using Dilations | Texas Gateway
  10. Real-World Applications - Similarity and dilations pop up everywhere - from map reading and model building to photography and art, they help us scale the world around us. Spotting these examples boosts your understanding and shows why geometry rules real life. Generating Similar Figures Using Dilations | Texas Gateway
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics Quizzes

Powered by: Quiz Maker