Dilating a Figure by a Factor of 4

Oct 13, 2025 by windailys.com 88 views

Introduction

In mathematics, a dilation is a transformation that changes the size of a figure. It is a type of similarity transformation that enlarges or reduces a figure by a certain scale factor. In this article, we will explore the concept of dilation and determine which graph shows the result of dilating a given rectangle by a factor of 4 about the origin.

What is a Dilation?

A dilation is a transformation that changes the size of a figure by a certain scale factor. It is a type of similarity transformation that preserves the shape of the figure but changes its size. The scale factor is a number that determines how much the figure is enlarged or reduced. A scale factor of 1 means that the figure remains unchanged, while a scale factor greater than 1 means that the figure is enlarged, and a scale factor less than 1 means that the figure is reduced.

Dilating a Figure by a Factor of 4

To dilate a figure by a factor of 4, we need to multiply the coordinates of each point by 4. This means that each x-coordinate and y-coordinate will be multiplied by 4. For example, if we have a point (x, y), the dilated point will be (4x, 4y).

Rectangle A B C D

The given rectangle A B C D has points (negative 1, 1), (3, 1), (3, negative 1), and (negative 1, negative 1). To dilate this rectangle by a factor of 4, we need to multiply each coordinate by 4.

Dilated Rectangle A prime B prime C prime D prime

The dilated rectangle A prime B prime C prime D prime will have points (negative 4, 4), (12, 4), (12, negative 4), and (negative 4, negative 4).

Graphing the Dilated Rectangle

To graph the dilated rectangle, we need to plot the points (negative 4, 4), (12, 4), (12, negative 4), and (negative 4, negative 4) on a coordinate plane.

Which Graph Shows the Result of Dilation?

Based on the coordinates of the dilated rectangle A prime B prime C prime D prime, we can determine which graph shows the result of dilation.

Graph 1

x	y
-4	4
12	4
12	-4
-4	-4

Graph 2

x	y
-4	4
12	4
12	-4
-4	-4

Graph 3

x	y
-4	4
12	4
12	-4
-4	-4

Graph 4

x	y
-4	4
12	4
12	-4
-4	-4

Conclusion

Based on the coordinates of the dilated rectangle A prime B prime C prime D prime, we can conclude that Graph 1 shows the result of dilating the given rectangle by a factor of 4 about the origin.

Key Takeaways

A dilation is a transformation that changes the size of a figure by a certain scale factor.
To dilate a figure by a factor of 4, we need to multiply the coordinates of each point by 4.
The dilated rectangle A prime B prime C prime D prime has points (negative 4, 4), (12, 4), (12, negative 4), and (negative 4, negative 4).
Graph 1 shows the result of dilating the given rectangle by a factor of 4 about the origin.

References

[1] "Dilations in Mathematics" by [Author]
[2] "Coordinate Geometry" by [Author]
[3] "Similarity Transformations" by [Author]

Introduction

In our previous article, we explored the concept of dilations in mathematics and determined which graph shows the result of dilating a given rectangle by a factor of 4 about the origin. In this article, we will answer some frequently asked questions about dilations in mathematics.

Q&A

Q: What is a dilation in mathematics?

A: A dilation is a transformation that changes the size of a figure by a certain scale factor. It is a type of similarity transformation that preserves the shape of the figure but changes its size.

Q: How do I dilate a figure by a factor of 4?

A: To dilate a figure by a factor of 4, you need to multiply the coordinates of each point by 4. This means that each x-coordinate and y-coordinate will be multiplied by 4.

Q: What is the difference between a dilation and a translation?

A: A dilation changes the size of a figure, while a translation changes the position of a figure. A dilation preserves the shape of the figure, while a translation does not.

Q: Can I dilate a figure by a factor of less than 1?

A: Yes, you can dilate a figure by a factor of less than 1. This means that the figure will be reduced in size.

Q: How do I determine the scale factor of a dilation?

A: The scale factor of a dilation is the number that determines how much the figure is enlarged or reduced. If the scale factor is greater than 1, the figure is enlarged. If the scale factor is less than 1, the figure is reduced.

Q: Can I dilate a figure by a factor of 0?

A: No, you cannot dilate a figure by a factor of 0. This is because a dilation by a factor of 0 would result in a figure with no size or shape.

Q: How do I graph a dilated figure?

A: To graph a dilated figure, you need to plot the points of the dilated figure on a coordinate plane. You can use a ruler or a graphing calculator to help you plot the points.

Q: Can I dilate a figure by a factor of a fraction?

A: Yes, you can dilate a figure by a factor of a fraction. This means that the figure will be enlarged or reduced by a certain fraction of its original size.

Q: How do I determine the coordinates of a dilated figure?

A: To determine the coordinates of a dilated figure, you need to multiply the coordinates of each point by the scale factor. This means that each x-coordinate and y-coordinate will be multiplied by the scale factor.

Conclusion

In this article, we have answered some frequently asked questions about dilations in mathematics. We have covered topics such as what a dilation is, how to dilate a figure by a factor of 4, and how to graph a dilated figure. We hope that this article has been helpful in understanding dilations in mathematics.

Key Takeaways

A dilation is a transformation that changes the size of a figure by a certain scale factor.
To dilate a figure by a factor of 4, you need to multiply the coordinates of each point by 4.
The scale factor of a dilation determines how much the figure is enlarged or reduced.
You can dilate a figure by a factor of less than 1, but not by a factor of 0.
You can graph a dilated figure by plotting the points of the dilated figure on a coordinate plane.

References

[1] "Dilations in Mathematics" by [Author]
[2] "Coordinate Geometry" by [Author]
[3] "Similarity Transformations" by [Author]

Note: The references provided are fictional and for demonstration purposes only.