Question
Dilating Figures Practice
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Question
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A coordinate plane's axes range from negative 1 to 4 by 1-unit increments. 4 points forming a rectangle are plotted. They are labeled upper A (1,1), upper B (0,2), upper C (2,4), and upper D (3,3), respectively.
Suppose you dilate the rectangle on the coordinate plane using a magnitude of 1/2
and the center of dilation at (1,1)
. What would be the corresponding ordered pair to the current point D
?
(1 point)
The new ordered pair for point D′
would be at ( , ).
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Complete this assessment to review what you’ve learned. It will not count toward your grade.
4 of 54 of 5 Items
Question
Use the image to answer the question.
A coordinate plane's axes range from negative 1 to 4 by 1-unit increments. 4 points forming a rectangle are plotted. They are labeled upper A (1,1), upper B (0,2), upper C (2,4), and upper D (3,3), respectively.
Suppose you dilate the rectangle on the coordinate plane using a magnitude of 1/2
and the center of dilation at (1,1)
. What would be the corresponding ordered pair to the current point D
?
(1 point)
The new ordered pair for point D′
would be at ( , ).
Remaining Attempts : 0
Skip to navigation
Answers
GPT-4o mini
To find the new coordinates for point D after dilation, we need to follow these steps:
1. **Identify the coordinates of point D**: The current coordinates of D are (3, 3).
2. **Identify the center of dilation**: The center of dilation is at (1, 1).
3. **Calculate the distance from the center of dilation to point D**:
- The distance in the x-direction: \( x_D - x_{center} = 3 - 1 = 2 \)
- The distance in the y-direction: \( y_D - y_{center} = 3 - 1 = 2 \)
4. **Apply the scale factor of the dilation**: Since the scale factor is \( \frac{1}{2} \), we multiply the distances by \( \frac{1}{2} \):
- New x-distance: \( 2 \times \frac{1}{2} = 1 \)
- New y-distance: \( 2 \times \frac{1}{2} = 1 \)
5. **Calculate the new coordinates**: We add the new distances to the center of dilation:
- New x-coordinate: \( x_{center} + \text{New x-distance} = 1 + 1 = 2 \)
- New y-coordinate: \( y_{center} + \text{New y-distance} = 1 + 1 = 2 \)
Thus, the new ordered pair for point D′ would be (2, 2).
1. **Identify the coordinates of point D**: The current coordinates of D are (3, 3).
2. **Identify the center of dilation**: The center of dilation is at (1, 1).
3. **Calculate the distance from the center of dilation to point D**:
- The distance in the x-direction: \( x_D - x_{center} = 3 - 1 = 2 \)
- The distance in the y-direction: \( y_D - y_{center} = 3 - 1 = 2 \)
4. **Apply the scale factor of the dilation**: Since the scale factor is \( \frac{1}{2} \), we multiply the distances by \( \frac{1}{2} \):
- New x-distance: \( 2 \times \frac{1}{2} = 1 \)
- New y-distance: \( 2 \times \frac{1}{2} = 1 \)
5. **Calculate the new coordinates**: We add the new distances to the center of dilation:
- New x-coordinate: \( x_{center} + \text{New x-distance} = 1 + 1 = 2 \)
- New y-coordinate: \( y_{center} + \text{New y-distance} = 1 + 1 = 2 \)
Thus, the new ordered pair for point D′ would be (2, 2).