It looks like you've uploaded an image of a worksheet titled
"4 Enlargements and 4 Reductions", which involves
transformations on the coordinate plane — specifically,
enlargements (dilations) and
reductions (contractions).
However, since I cannot view or access images directly, I can't see the specific details of the task, such as:
- The original shapes
- The center of dilation
- The scale factors
- The coordinates of points
But I can help you solve this type of problem
if you describe it. Here’s how to approach
enlargements and reductions (dilations) on the coordinate plane:
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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 uses a
scale factor and a
center of dilation.
- If the
scale factor > 1, it's an
enlargement.
- If the
scale factor between 0 and 1, it's a
reduction.
- If the
scale factor is negative, the image is also reflected.
---
🔷 How to Perform a Dilation
Let’s say:
- You have a point $ A(x, y) $
- The
center of dilation is at $ C(a, b) $
- The
scale factor is $ k $
Then the new point $ A' $ after dilation is:
$$
A'(x', y') = \left( a + k(x - a),\ b + k(y - b) \right)
$$
If the center is the
origin (0, 0), this simplifies to:
$$
A'(x', y') = (kx, ky)
$$
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✔ Step-by-Step Example
Suppose:
- Triangle ABC has points: $ A(2, 1), B(4, 3), C(1, 5) $
- Center of dilation: origin (0, 0)
- Scale factor: $ k = 2 $ (enlargement)
Then:
- $ A' = (2×2, 1×2) = (4, 2) $
- $ B' = (4×2, 3×2) = (8, 6) $
- $ C' = (1×2, 5×2) = (2, 10) $
Plot these new points and connect them — you now have an enlarged triangle.
For a
reduction, use $ k = 0.5 $, for example.
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📌 Tips for Solving This Worksheet
1.
Identify the scale factor (e.g., 2, 3, 0.5, 1/3).
2.
Find the center of dilation (often origin or a given point).
3.
Apply the dilation formula to each vertex.
4.
Plot the new points and draw the transformed shape.
5.
Label the image (e.g., A'B'C').
---
❓ What Do You Need?
To help you fully, please provide:
1. The
coordinates of the original points
2. The
scale factor(s) used
3. The
center of dilation
4. Whether the problem asks for
enlargements only,
reductions only, or both
Once you give me that info, I’ll walk you through solving each part step by step.
Alternatively, if you can describe what’s on the worksheet, I’ll guide you through the process!
Parent Tip: Review the logic above to help your child master the concept of dilations on the coordinate plane worksheet.
