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Quizzes > High School Quizzes > Mathematics

Dilations Practice Quiz for 8th Grade

Master dilations with our interactive practice worksheet

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting a Dilations Demystified trivia quiz for high school geometry students.

What is a dilation in geometry?
A transformation that enlarges or reduces a figure by a scale factor about a center.
A transformation that rotates a figure around a point.
A transformation that shifts a figure from one location to another.
A transformation that reflects a figure across a line.
A dilation is a transformation that resizes a figure while preserving its shape. It uses a scale factor relative to a fixed center, which makes the last option the correct definition.
In a dilation, what does the scale factor represent?
The degree of rotation applied.
The fixed distance the figure moves.
The angle by which the figure is reflected.
The factor by which all distances from the center are multiplied.
The scale factor determines how much every distance from the center of dilation is multiplied, thereby enlarging or reducing the figure. This explanation confirms that option three is correct.
What is the center of dilation?
The point that remains invariant under translation.
The point where the figure is reflected.
The midpoint of every side of the figure.
The fixed point about which the figure is enlarged or reduced.
The center of dilation is the fixed point used as a reference during the transformation, meaning it does not move while all other points scale relative to it. This makes the second option correct.
Which property is preserved during a dilation?
The distance between all points.
The location of each vertex.
The size of the figure.
The shape of the figure.
Dilations change the size of a figure but preserve its overall shape by keeping the angles and the proportionality of sides intact. Therefore, option two is the accurate statement.
If a point has coordinates (x, y), what are its coordinates after a dilation with scale factor k centered at the origin?
(x + k, y + k).
(x/k, y/k).
It remains (x, y).
(kx, ky).
When dilating about the origin, each coordinate of the point is multiplied by the scale factor, resulting in new coordinates of (kx, ky). This confirms that option B is correct.
Which statement is true about a dilation with a scale factor less than 1?
It reflects the figure.
It rotates the figure.
It reduces the figure's size.
It enlarges the figure.
A dilation with a scale factor less than 1 makes the figure smaller by reducing every distance from the center. This means the figure is contracted, making option two the correct answer.
When the center of dilation is not at the origin, which of the following describes how to obtain the coordinates of a dilated point?
Subtract the center, multiply by the scale factor, then add the center back.
The coordinates remain unchanged.
Multiply the original coordinates by the scale factor.
Divide the coordinates by the scale factor.
When the center of dilation is not at the origin, you must first translate the point by subtracting the center coordinates, apply the scale factor, and then translate back by adding the center. This process is accurately described in option three.
For two similar figures under dilation, how does the perimeter of the image relate to the perimeter of the original?
They are reduced by a fixed amount.
They are scaled by the square of the scale factor.
They remain identical.
They are scaled by the same factor as the sides.
A dilation multiplies all linear measurements by the scale factor, which means the perimeter of a figure scales directly with that factor. Option two clearly states this relationship.
How does a dilation affect the area of a figure?
It divides the area by the scale factor.
It multiplies the area by the square of the scale factor.
It leaves the area unchanged.
It multiplies the area by the scale factor.
Since area is a two-dimensional measure, every linear dimension is multiplied by the scale factor, resulting in the area being multiplied by the square of that factor. This makes option one correct.
What happens to the angles of a triangle when it undergoes a dilation?
The angles remain identical to the original triangle's angles.
The angles are rearranged in a different order.
All angles increase uniformly.
All angles decrease uniformly.
Dilation is a similarity transformation, which means that while the size of the figure changes, the angle measures do not. Option three correctly identifies that the angles remain intact.
Which property is not preserved during a dilation?
Proportionality of side lengths.
Exact distances between corresponding points.
Angle measurements.
Parallelism of lines.
While dilations preserve the shape and proportional relationships of a figure, the specific distances between points change according to the scale factor. This makes option three the correct choice.
If a line segment has an original length L, what will be its new length after a dilation with scale factor k?
L * k
L + k
L/k
L - k
Dilation scales all linear dimensions by the scale factor, so a segment of length L becomes L multiplied by k. The second option correctly represents this relationship.
What is the image of the point (3,4) after a dilation by a factor of 2 with center at (1,1)?
(3, 4)
(5, 7)
(6, 8)
(7, 9)
To find the dilated coordinates, subtract the center (1,1) from (3,4) to get (2,3), multiply by the scale factor to obtain (4,6), and then add the center back for a result of (5,7). This makes option two correct.
Why are dilations classified as similarity transformations?
They preserve the proportions and angle measures.
They modify color but not geometry.
They change both side lengths and angles.
They alter the shape of figures.
Dilations maintain the proportionality of side lengths and preserve the measures of angles, which means the resulting figure is similar to the original. Option three accurately reflects this concept.
What is the effect of a dilation on the slope of a non-vertical line?
The slope remains unchanged.
The slope is multiplied by the scale factor.
The slope becomes zero.
The slope is inverted.
Dilations uniformly scale distances without altering the angles between lines. Since the slope is determined by the angle of the line, it remains the same after dilation, making option three correct.
If a square with side length s is dilated by a factor of 3 from its center, what is the area of the resulting square?
9 times the original area.
3 times the original area.
6 times the original area.
12 times the original area.
Dilating a square by a factor of 3 increases the side length to 3s, so the area becomes (3s)^2 = 9s^2, which is 9 times the original area. Option two is therefore correct.
A dilation is applied with a negative scale factor. What additional effect does this have on the image of a figure?
It rotates the image by 90 degrees.
It reflects the image through the center of dilation in addition to scaling.
It leaves the image unchanged.
It only reduces the image's size.
A negative scale factor not only scales the figure but also introduces a reflection through the center of dilation. This combined effect is accurately described in option two.
Given a dilation with a positive scale factor k, what condition must be met for the transformation to be considered a contraction?
k = 1
k > 1
k < 0
0 < k < 1
A contraction reduces the size of a figure, which occurs when the scale factor is between 0 and 1. Thus, the correct condition is given in option three.
A triangle with vertices (0,0), (4,0), and (0,3) is dilated by a factor of 2 about the point (1,1). What are the coordinates of the image of the vertex (4,0)?
(9, -2)
(5, 1)
(7, -1)
(1, 1)
Subtracting the center (1,1) from (4,0) gives (3, -1). Multiplying by 2 gives (6, -2), and adding the center back yields (7, -1). This confirms that option one is correct.
A dilation maps a circle to a new circle whose area is 16 times larger than the original. What is the scale factor of the dilation?
16
8
4
2
Because the area of a circle scales by the square of the dilation factor, an increase in area by a factor of 16 indicates a scale factor of √16 = 4. Hence, option two is the correct answer.
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Study Outcomes

  1. Understand the definition and properties of dilations in geometry.
  2. Identify the center of dilation and corresponding scale factors in various problems.
  3. Apply dilation principles to transform geometric figures accurately.
  4. Analyze the relationship between pre-images and images resulting from dilations.
  5. Evaluate the impact of different scale factors on the size and orientation of shapes.

Dilations Practice Quiz for 8th Grade Cheat Sheet

  1. Dilations keep shapes similar - A dilation scales a figure up or down, changing its size but leaving its shape untouched. Think of it as your favorite cartoon character going through a magic resizing spell - same character, different size! Dilation in Geometry
  2. Center of dilation is your anchor point - The center of dilation is the fixed spot from which all points on a figure move closer or farther away. Imagine a rubber sheet pinned at one spot; everything else stretches or shrinks around that pin! Understanding Dilations
  3. Scale factor decides big or small - The scale factor tells you how much to enlarge (>1) or reduce (between 0 and 1) a figure. It's like turning a dial: crank it past 1 to blow things up, or dial it down for a miniature edition! Dilations & Scale Factor
  4. Dilate on the coordinate plane - When your center of dilation is the origin (0, 0), simply multiply each (x, y) coordinate by your scale factor. It's as easy as plugging numbers into a calculator and watching your shape grow or shrink! Coordinate Plane Dilations
  5. Off-origin dilations need translation - If the center isn't the origin, slide (translate) your figure so the center sits at (0, 0), apply the dilation, then slide it back. Think of moving furniture, resizing it, and then moving it to its original spot! Dilations Off the Origin
  6. Angles stay perfect - Dilation never messes with angles, so the pre-image and image remain similar. It's like photocopying a shape at a different zoom level - the angles are still spot-on! Angle Preservation in Dilations
  7. Use the dilation formula - For a center at (a, b) and scale factor k, transform each point (x, y) to (k(x - a)+a, k(y - b)+b). This formula is your secret weapon for pinpoint precision! Dilation Formula Worksheet
  8. Spot dilations in real life - From resizing photos to scaling architectural models, dilations are everywhere. Next time you zoom in on Instagram, pat yourself on the back - you're seeing a dilation in action! Real-World Dilations
  9. Play with interactive tools - Websites like GeoGebra let you drag, stretch, and shrink shapes live. Jump in, tinker with the scale factor, and watch your figures come to life! Interactive Dilations
  10. Quiz yourself with practice problems - Test your mastery by finding scale factors and performing dilations on various shapes. Challenge accepted? Grab some practice questions and go for gold! Dilations Practice Questions
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