A Dilation With The Rule { (x, Y) \rightarrow (4x, 4y)$}$ And Centered At The Origin Is Applied To { \overline{AB}$}$ With Endpoints { A(1,3)$}$ And { B(5,3)$}$.Drag And Drop To Match Each Point With Its Correct
A Dilation with a Scale Factor of 4: Understanding the Transformation of Line Segment AB
In geometry, a dilation is a transformation that changes the size of a figure, but not its shape. It is a type of similarity transformation that involves scaling the coordinates of the figure's points. In this article, we will explore the concept of dilation with a scale factor of 4 and apply it to a line segment AB with endpoints A(1,3) and B(5,3).
What is a Dilation?
A dilation is a transformation that maps a point (x, y) to a new point (kx, ky), where k is the scale factor. In this case, the scale factor is 4, which means that each coordinate of the point will be multiplied by 4. This results in a new point with coordinates (4x, 4y).
The Dilation Rule
The dilation rule is given by the equation (x, y) → (4x, 4y). This means that for any point (x, y), we multiply its x-coordinate by 4 and its y-coordinate by 4 to get the new point (4x, 4y).
Applying the Dilation to Line Segment AB
To apply the dilation to line segment AB, we need to find the new coordinates of points A and B. We can do this by multiplying the x and y coordinates of each point by 4.
- For point A(1,3), the new coordinates are (4(1), 4(3)) = (4, 12).
- For point B(5,3), the new coordinates are (4(5), 4(3)) = (20, 12).
The New Line Segment AB
After applying the dilation, the new line segment AB has endpoints A'(4, 12) and B'(20, 12). We can see that the line segment has been stretched by a factor of 4 in both the x and y directions.
Understanding the Transformation
The dilation transformation has changed the size of line segment AB, but not its shape. The line segment is still a straight line, but it has been stretched to a new length. This is because the dilation transformation preserves the angles and shapes of the original figure.
Key Takeaways
- A dilation is a transformation that changes the size of a figure, but not its shape.
- The dilation rule is given by the equation (x, y) → (kx, ky), where k is the scale factor.
- The dilation transformation preserves the angles and shapes of the original figure.
- The scale factor determines the amount of stretching or shrinking that occurs during the dilation.
In conclusion, a dilation with a scale factor of 4 has been applied to line segment AB with endpoints A(1,3) and B(5,3). The new line segment AB has endpoints A'(4, 12) and B'(20, 12). This transformation has changed the size of the line segment, but not its shape. We hope that this article has provided a clear understanding of the concept of dilation and its application to line segments.
| Point | Image |
|---|---|
| A(1,3) | A'(4, 12) |
| B(5,3) | B'(20, 12) |
Drag and Drop to Match Each Point with Its Correct Image
Drag the points from the left column to the right column to match each point with its correct image.
| Point | Image |
|---|---|
| A(1,3) | A'(4, 12) |
| B(5,3) | B'(20, 12) |
Drag and Drop Instructions
- Drag the points from the left column to the right column.
- Match each point with its correct image.
- Click on the "Submit" button to check your answers.
Tips and Tricks
- Make sure to read the instructions carefully before starting the activity.
- Take your time and match each point with its correct image carefully.
- If you are unsure about an answer, try dragging the point to a different image and see if it looks correct.
In conclusion, we have applied a dilation with a scale factor of 4 to line segment AB with endpoints A(1,3) and B(5,3). The new line segment AB has endpoints A'(4, 12) and B'(20, 12). We hope that this article has provided a clear understanding of the concept of dilation and its application to line segments.
A Dilation with a Scale Factor of 4: Understanding the Transformation of Line Segment AB
Q: What is a dilation?
A: A dilation is a transformation that changes the size of a figure, but not its shape. It is a type of similarity transformation that involves scaling the coordinates of the figure's points.
Q: What is the dilation rule?
A: The dilation rule is given by the equation (x, y) → (kx, ky), where k is the scale factor. In this case, the scale factor is 4, which means that each coordinate of the point will be multiplied by 4.
Q: How do I apply the dilation to a line segment?
A: To apply the dilation to a line segment, you need to find the new coordinates of the endpoints of the line segment. You can do this by multiplying the x and y coordinates of each point by the scale factor.
Q: What happens to the shape of the line segment after the dilation?
A: The dilation transformation preserves the angles and shapes of the original figure. This means that the line segment will still be a straight line, but it will have been stretched to a new length.
Q: How do I find the new coordinates of the endpoints of the line segment?
A: To find the new coordinates of the endpoints of the line segment, you need to multiply the x and y coordinates of each point by the scale factor. For example, if the original coordinates of a point are (x, y), the new coordinates will be (4x, 4y).
Q: What is the scale factor in this dilation?
A: The scale factor in this dilation is 4. This means that each coordinate of the point will be multiplied by 4 to get the new point.
Q: How do I determine the amount of stretching or shrinking that occurs during the dilation?
A: The amount of stretching or shrinking that occurs during the dilation is determined by the scale factor. In this case, the scale factor is 4, which means that the line segment will be stretched by a factor of 4 in both the x and y directions.
Q: What is the new line segment after the dilation?
A: The new line segment after the dilation has endpoints A'(4, 12) and B'(20, 12). This line segment has been stretched by a factor of 4 in both the x and y directions.
Q: How do I match each point with its correct image after the dilation?
A: To match each point with its correct image after the dilation, you need to drag the points from the left column to the right column. Make sure to match each point with its correct image carefully.
Q: What are some tips and tricks for matching each point with its correct image?
A: Here are some tips and tricks for matching each point with its correct image:
- Make sure to read the instructions carefully before starting the activity.
- Take your time and match each point with its correct image carefully.
- If you are unsure about an answer, try dragging the point to a different image and see if it looks correct.
In conclusion, we have answered some common questions about dilation with a scale factor of 4. We hope that this article has provided a clear understanding of the concept of dilation and its application to line segments.