It looks like you've uploaded a preview image of a worksheet titled
"Clear, Easy to Read Coordinate Planes", which contains several dilation problems involving coordinate geometry. However, the actual image is marked with "Preview," so I cannot see the full details of the shapes or coordinates.
But based on what's visible, here’s how to solve such problems and an explanation of the concepts involved:
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🔍 What Is a Dilation?
A
dilation is a transformation that changes the size of a figure while keeping its shape the same. It involves:
- A
center of dilation (a fixed point)
- A
scale factor (how much bigger or smaller the figure becomes)
If the scale factor is greater than 1, the figure gets larger. If it's between 0 and 1, it gets smaller.
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✔ Steps to Solve a Dilation Problem
Let’s go through each problem type shown in your image.
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#### 🔹 Problem 2: Dilate kite EFGH
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Center of dilation: (0, 0)
-
Scale factor: 2
How to do it:
1. Identify the coordinates of points E, F, G, H.
2. Multiply each coordinate by the scale factor (2).
- Example: If E is at (1, 3), then E' = (1×2, 3×2) = (2, 6)
3. Plot the new points E', F', G', H'.
4. Connect them to form the dilated kite.
> Since the center is (0,0), this is a
central dilation — just multiply x and y by the scale factor.
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#### 🔹 Problem 7: Dilate rectangle EFGH
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Center of dilation: Point P
-
Scale factor: ½
How to do it:
1. Find coordinates of E, F, G, H.
2. Find coordinates of point P (the center).
3. Use the
dilation formula:
$$
(x', y') = (P_x + k(x - P_x), P_y + k(y - P_y))
$$
where $k = \frac{1}{2}$
This means:
- Subtract P’s coordinates from each point.
- Multiply by ½.
- Add back P’s coordinates.
Example:
- If E = (4, 6), P = (2, 2), then:
$$
E' = (2 + ½(4 - 2), 2 + ½(6 - 2)) = (2 + 1, 2 + 2) = (3, 4)
$$
4. Do this for all points and draw the new rectangle.
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#### 🔹 Problem 4: Dilate triangle LMN
-
Center of dilation: (0, 0)
-
Scale factor: 2
Same as Problem 2:
- Multiply each vertex coordinate by 2.
- For example:
- L = (1, 1) → L' = (2, 2)
- M = (3, 1) → M' = (6, 2)
- N = (2, 4) → N' = (4, 8)
Plot and connect the new points.
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🧩 General Tips:
- Always label the original and dilated figures clearly.
- Use grid lines carefully to ensure accuracy.
- Double-check calculations, especially when the center isn’t the origin.
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❓ But Wait — You Said “I Uploaded an Image”...
Since the image says
"Preview", I can't see the exact coordinates of the points (E, F, G, H, etc.). So I can't give specific answers unless you provide:
- The coordinates of the original points
- Or describe the locations on the grid
- Or upload the full image
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✔ How to Help Me Solve It:
Please either:
1. Provide the coordinates of the points (e.g., E = (1, 2), F = (3, 4), etc.)
2. Describe the positions of the shapes on the grid
3. Upload a clear version of the image without the "Preview" watermark
Then I’ll solve it step-by-step with exact answers!
Would you like to proceed?
Parent Tip: Review the logic above to help your child master the concept of dilations on the coordinate plane worksheet.
