The Pre-image Of A Right Triangle Has A Base Of 10 Inches And A Height Of 8 Inches. The Image Has A Base Of 15 Inches And A Height Of 12 Inches. What Is The Scale Factor Used In The Dilation?A. 3 5 \frac{3}{5} 5 3 B. 4 5 \frac{4}{5} 5 4 C.
Understanding the Concept of Dilation
Dilation is a transformation that changes the size of a figure. In this case, we are dealing with a right triangle that has undergone a dilation. The pre-image of the right triangle has a base of 10 inches and a height of 8 inches, while the image has a base of 15 inches and a height of 12 inches. Our goal is to find the scale factor used in the dilation.
What is a Scale Factor?
A scale factor is a ratio that describes the size of the image in relation to the pre-image. It is calculated by dividing the length of a corresponding side of the image by the length of the corresponding side of the pre-image. In this case, we need to find the scale factor that relates the base and height of the pre-image to the base and height of the image.
Calculating the Scale Factor
To calculate the scale factor, we can use the formula:
Scale Factor = (Length of corresponding side of image) / (Length of corresponding side of pre-image)
We can apply this formula to the base and height of the right triangle. Let's start with the base:
Scale Factor (base) = (15 inches) / (10 inches) = 1.5
Next, let's calculate the scale factor for the height:
Scale Factor (height) = (12 inches) / (8 inches) = 1.5
Finding the Scale Factor Used in the Dilation
Since the scale factor for the base and height are the same, we can conclude that the scale factor used in the dilation is 1.5. This means that the image is 1.5 times larger than the pre-image.
Why is the Scale Factor Important?
The scale factor is an important concept in geometry and is used to describe the size and shape of figures. It is used in a variety of applications, including architecture, engineering, and art. Understanding the scale factor is crucial in these fields, as it allows us to create accurate models and designs.
Real-World Applications of Dilation
Dilation has many real-world applications, including:
- Architecture: Dilation is used in architecture to create scale models of buildings and structures.
- Engineering: Dilation is used in engineering to create scale models of machines and mechanisms.
- Art: Dilation is used in art to create scale models of sculptures and other three-dimensional objects.
Conclusion
In conclusion, the scale factor used in the dilation of a right triangle is 1.5. This means that the image is 1.5 times larger than the pre-image. Understanding the scale factor is crucial in geometry and has many real-world applications.
Final Answer
The final answer is:
Understanding the Concept of Dilation
Dilation is a transformation that changes the size of a figure. In this case, we are dealing with a right triangle that has undergone a dilation. The pre-image of the right triangle has a base of 10 inches and a height of 8 inches, while the image has a base of 15 inches and a height of 12 inches. Our goal is to find the scale factor used in the dilation.
Q&A: The Scale Factor of Dilation
Q: What is a scale factor?
A: A scale factor is a ratio that describes the size of the image in relation to the pre-image. It is calculated by dividing the length of a corresponding side of the image by the length of the corresponding side of the pre-image.
Q: How do I calculate the scale factor?
A: To calculate the scale factor, you can use the formula:
Scale Factor = (Length of corresponding side of image) / (Length of corresponding side of pre-image)
Q: What is the scale factor used in the dilation of a right triangle?
A: The scale factor used in the dilation of a right triangle is 1.5. This means that the image is 1.5 times larger than the pre-image.
Q: Why is the scale factor important?
A: The scale factor is an important concept in geometry and is used to describe the size and shape of figures. It is used in a variety of applications, including architecture, engineering, and art.
Q: What are some real-world applications of dilation?
A: Dilation has many real-world applications, including:
- Architecture: Dilation is used in architecture to create scale models of buildings and structures.
- Engineering: Dilation is used in engineering to create scale models of machines and mechanisms.
- Art: Dilation is used in art to create scale models of sculptures and other three-dimensional objects.
Q: How do I find the scale factor used in the dilation of a figure?
A: To find the scale factor used in the dilation of a figure, you can use the formula:
Scale Factor = (Length of corresponding side of image) / (Length of corresponding side of pre-image)
You can apply this formula to the base and height of the figure to find the scale factor.
Q: What is the difference between dilation and other transformations?
A: Dilation is a transformation that changes the size of a figure, but not its shape. Other transformations, such as translation and rotation, change the position or orientation of a figure, but not its size.
Conclusion
In conclusion, the scale factor used in the dilation of a right triangle is 1.5. This means that the image is 1.5 times larger than the pre-image. Understanding the scale factor is crucial in geometry and has many real-world applications.
Final Answer
The final answer is: