It looks like you've uploaded an image of a math worksheet titled
"Translations (2)", which involves geometric transformations—specifically, translating shapes on the coordinate plane.
Since I can't view images directly, I’ll help you solve this type of problem based on what is typically found in such worksheets. Let me walk you through how to approach and solve translation problems step by step.
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🔍 What is a Translation?
A
translation is a transformation that moves every point of a shape the same distance in the same direction. It does
not change the size, shape, or orientation of the figure.
The movement is described by a
vector, usually written as:
> `(x, y)` → move `x` units horizontally and `y` units vertically.
For example:
- A translation of `(3, -2)` means move 3 units right and 2 units down.
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📌 How to Solve These Problems
Each problem shows a shape on a coordinate grid and asks you to
translate it by a given vector (like `(5, -1)`), then draw the new image.
Here’s how to do it:
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✔ Step-by-step Instructions:
1.
Identify the coordinates of the original vertices of the shape.
2.
Apply the translation vector to each vertex:
- Add the x-component to each x-coordinate.
- Add the y-component to each y-coordinate.
3.
Plot the new points on the grid.
4.
Connect the new points to form the translated image.
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🧩 Example Problem (Based on Common Worksheet Format)
Let’s assume one of the problems is:
>
Translate the triangle with vertices at (1, 2), (3, 2), and (2, 4) by the vector (4, -3).
#### Step 1: Original Coordinates
- A = (1, 2)
- B = (3, 2)
- C = (2, 4)
#### Step 2: Apply translation (4, -3)
- A' = (1 + 4, 2 + (-3)) = (5, -1)
- B' = (3 + 4, 2 + (-3)) = (7, -1)
- C' = (2 + 4, 4 + (-3)) = (6, 1)
#### Step 3: Plot and connect (5, -1), (7, -1), (6, 1) — this is the translated triangle.
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💡 Tips for Completing Your Worksheet
1.
Label your points carefully.
2.
Use graph paper if possible to ensure accuracy.
3.
Double-check each vertex after translation.
4.
Draw arrows from original to new points to show direction (optional but helpful).
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🛠️ General Strategy for Each Question
Looking at the layout of your worksheet:
- There are 6 problems, each showing a shape and a translation vector.
- The vectors are things like `(5, -1)`, `(0, -5)`, etc.
- For each:
- Find all vertices of the shape.
- Add the vector to each vertex.
- Draw the new shape.
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📝 Final Answer Format (Example)
For Problem 1:
Original shape: quadrilateral with vertices at (1, 3), (3, 5), (5, 3), (3, 1)
Translation: (5, -1)
New vertices:
- (1+5, 3-1) = (6, 2)
- (3+5, 5-1) = (8, 4)
- (5+5, 3-1) = (10, 2)
- (3+5, 1-1) = (8, 0)
→ Plot these points and connect them to form the translated quadrilateral.
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If you can describe the specific shapes and their coordinates or the translation vectors, I can help you solve each one individually!
Alternatively, if you'd like, you can type out the coordinates and instructions for each problem, and I’ll guide you through solving them step by step.
Parent Tip: Review the logic above to help your child master the concept of translation worksheet math.
