You change the size of a shape using scale factors by multiplying its side lengths.
Understanding and applying scale factors is a fundamental concept in geometry used to resize figures while maintaining their shape. It's not about changing the scale factor number itself, but rather about using a chosen scale factor to modify the dimensions of a shape.
Applying a Scale Factor: The Process
The core method for applying a scale factor to a shape is straightforward:
- To scale a shape up or down, you multiply every side length of a shape by the scale factor to increase or decrease the size.
This means if you have a shape with sides of length A, B, and C, and you apply a scale factor of k, the new shape will have corresponding side lengths of Ak, Bk, and Ck.
What Happens to the Shape?
When you apply a scale factor:
- Side Lengths: All corresponding side lengths of the original shape are multiplied by the scale factor.
- Angles: The sizes of the angles do not change. The shape remains proportionally the same, just larger or smaller.
- Size: The overall size of the shape changes based on the scale factor value:
- Changing a shape by a scale factor greater than 1 will make the shape a larger figure. This is an enlargement.
- A scale factor between 0 and 1 (a fraction or decimal) will make the shape a smaller figure. This is a reduction.
- A scale factor of 1 means the shape remains the same size.
Example of Scaling a Shape
Let's consider a simple rectangle with side lengths 4 units and 6 units.
| Original Dimension | Operation | Scaled Dimension (Factor = 2) | Scaled Dimension (Factor = 0.5) |
|---|---|---|---|
| Length = 6 | Multiply by Scale Factor | 6 * 2 = 12 | 6 * 0.5 = 3 |
| Width = 4 | Multiply by Scale Factor | 4 * 2 = 8 | 4 * 0.5 = 2 |
In this example:
- Using a scale factor of 2 (greater than 1) created a larger rectangle with sides 12 and 8.
- Using a scale factor of 0.5 (between 0 and 1) created a smaller rectangle with sides 3 and 2.
- The angles of the rectangle (all 90 degrees) remain unchanged in both scaled versions.
In essence, changing the scale factor you apply directly changes the resulting size of the shape.
