Question

1. give an example of a scale factor that produces an enlargement. explain why you chose this scale factor
2. give an example of a scale factor that produces a reduction. explain why you chose this scale factor
3. give an example of a scale factor that produces an identical scale drawing. explain why you chose this scale factor
4. create a scale drawing of the figure shown on the grid. use a scale factor of 1 1/2

Explanation:

Step1: For enlargement

A scale - factor greater than 1 produces an enlargement. For example, a scale - factor of 2. When we multiply the dimensions of an original figure by 2, each side length becomes twice as long, thus creating an enlarged figure.

Step2: For reduction

A scale - factor between 0 and 1 produces a reduction. For example, a scale - factor of $\frac{1}{2}$. When we multiply the dimensions of an original figure by $\frac{1}{2}$, each side length becomes half as long, thus creating a reduced figure.

Step3: For identical drawing

A scale - factor of 1 produces an identical scale drawing. When we multiply the dimensions of an original figure by 1, the side lengths remain the same, so the new figure is identical to the original.

Step4: For creating scale drawing with scale factor $1\frac{1}{2}=\frac{3}{2}$

If the original square has side - length $s$ (say $s = 3$ grid units in the given grid). The new side - length of the square in the scale drawing is $s_{new}=s\times\frac{3}{2}=3\times\frac{3}{2} = 4.5$ grid units. We measure and draw a square with side - length 4.5 grid units.

Answer:

1. Example: 2. Reason: A scale - factor greater than 1 enlarges the figure.
2. Example: $\frac{1}{2}$. Reason: A scale - factor between 0 and 1 reduces the figure.
3. Example: 1. Reason: A scale - factor of 1 keeps the figure the same.
4. Measure and draw a square with side - length 4.5 grid units if the original square has side - length 3 grid units (assuming the original square side - length is measured in grid units).