Enlargements worksheet | PPT - Free Printable

To solve the problem of enlarging all shapes from the center of enlargement \( A \) by the given scale factors, we need to follow these steps:

Step 1: Understand the Problem

- We are given several shapes on a grid.
- Each shape has a center of enlargement marked as \( A \).
- We need to enlarge each shape by a specific scale factor.
- The scale factor determines how much larger (or smaller) the new shape will be compared to the original.

Step 2: Key Concepts

1. Center of Enlargement (\( A \)): All points of the shape are moved away from or towards this point based on the scale factor.
2. Scale Factor:
- If the scale factor is greater than 1, the shape is enlarged.
- If the scale factor is less than 1, the shape is reduced in size.
- The scale factor tells us how many times farther each point on the shape is from the center of enlargement compared to its original position.

Step 3: Procedure for Enlargement

For each shape:
1. Identify the coordinates of each vertex of the shape relative to the center of enlargement \( A \).
2. Multiply the distance of each vertex from \( A \) by the scale factor.
3. Plot the new vertices and connect them to form the enlarged shape.

Step 4: Solve Each Shape Individually

#### Shape 1: Triangle (Scale Factor = 2)
- Identify the vertices of the triangle relative to \( A \).
- Multiply the distances of each vertex from \( A \) by 2.
- Plot the new vertices and draw the enlarged triangle.

#### Shape 2: Diamond (Scale Factor = 4)
- Identify the vertices of the diamond relative to \( A \).
- Multiply the distances of each vertex from \( A \) by 4.
- Plot the new vertices and draw the enlarged diamond.

#### Shape 3: Square (Scale Factor = 2)
- Identify the vertices of the square relative to \( A \).
- Multiply the distances of each vertex from \( A \) by 2.
- Plot the new vertices and draw the enlarged square.

#### Shape 4: Rhombus (Scale Factor = 3)
- Identify the vertices of the rhombus relative to \( A \).
- Multiply the distances of each vertex from \( A \) by 3.
- Plot the new vertices and draw the enlarged rhombus.

#### Shape 5: Hexagon (Scale Factor = 3)
- Identify the vertices of the hexagon relative to \( A \).
- Multiply the distances of each vertex from \( A \) by 3.
- Plot the new vertices and draw the enlarged hexagon.

#### Shape 6: "L" Shape (Scale Factor = 2)
- Identify the vertices of the "L" shape relative to \( A \).
- Multiply the distances of each vertex from \( A \) by 2.
- Plot the new vertices and draw the enlarged "L" shape.

#### Shape 7: Rectangle (Scale Factor = 4)
- Identify the vertices of the rectangle relative to \( A \).
- Multiply the distances of each vertex from \( A \) by 4.
- Plot the new vertices and draw the enlarged rectangle.

#### Shape 8: Trapezoid (Scale Factor = \( \frac{1}{2} \))
- Identify the vertices of the trapezoid relative to \( A \).
- Multiply the distances of each vertex from \( A \) by \( \frac{1}{2} \).
- Plot the new vertices and draw the reduced trapezoid.

Step 5: Final Answer

The solution involves drawing each enlarged shape on the grid. Since I cannot physically draw the shapes here, the final answer is the process described above. If you were to perform this task manually, you would follow these steps for each shape.

$$
\boxed{\text{Follow the steps outlined above to enlarge each shape.}}
$$

If you need further clarification or assistance with any specific shape, feel free to ask!