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\frac{3}{4}.

Explanation:

Step1: Recall scale - factor rules for enlargement

A scale factor greater than 1 produces an enlargement. For example, a scale factor of 2 doubles the size of the figure.

Step2: Recall scale - factor rules for reduction

A scale factor between 0 and 1 produces a reduction. For example, a scale factor of $\frac{1}{2}$ halves the size of the figure.

Step3: Recall scale - factor for identical drawing

A scale factor of 1 produces an identical scale drawing since multiplying the dimensions of the original figure by 1 gives the same dimensions.

Step4: Create scale drawing for given factor

For a scale factor of $1\frac{3}{4}=\frac{7}{4}$, if the original figure has side - length $s$, the new side - length of the scale drawing is $s\times\frac{7}{4}$. Suppose the original square in the grid has side - length 4 units. The new side - length of the square in the scale drawing is $4\times\frac{7}{4}=7$ units.

Answer:

1. Example of scale factor for enlargement: 2. Reason: Since 2 > 1, it multiplies the dimensions of the original figure to make it larger.
2. Example of scale factor for reduction: $\frac{1}{2}$. Reason: Since $0<\frac{1}{2}<1$, it makes the new figure smaller than the original.
3. Example of scale factor for identical drawing: 1. Reason: Multiplying the dimensions of the original figure by 1 keeps the figure the same size.
4. (Actual drawing cannot be provided here, but if the original square has side - length $n$ units, the new square in the scale drawing has side - length $n\times\frac{7}{4}$ units. For example, if the original square has side - length 4 units, the new square has side - length 7 units).