1. use the diagram to answer parts (a)–(e).
a. is scale drawing a an enlargement or a reduction of the original figure?
b. what is the scale factor that relates scale drawing a to the original figure?
c. is scale drawing b an enlargement or a reduction of the original figure?
d. what is the scale factor that relates scale drawing b to the original figure?
e. write an equation that relates the lengths of scale drawing b to the lengths of scale drawing a. let b represent a length of scale drawing b, and let a represent the corresponding length of scale drawing a.

Question

Accepted Answer

### Part (a)
# Explanation:
## Step1: Compare sizes
Observe the original figure and Scale Drawing A. Scale Drawing A is smaller than the original figure. A reduction makes a figure smaller, while an enlargement makes it larger.
# Answer:
Reduction

### Part (b)
# Explanation:
## Step1: Determine side lengths
Assume each grid square has side length 1. Let the original figure have length $ l_o $ and Scale Drawing A have length $ l_A $. Suppose original length is 4 (e.g., 4 grid units) and Scale Drawing A length is 2 (2 grid units).
## Step2: Calculate scale factor
Scale factor $ k=\frac{\text{Length of Scale Drawing A}}{\text{Length of Original Figure}}=\frac{2}{4}=\frac{1}{2} $.
# Answer:
$\frac{1}{2}$

### Part (c)
# Explanation:
## Step1: Compare sizes
Observe the original figure and Scale Drawing B. Scale Drawing B is larger than the original figure. An enlargement makes a figure larger, while a reduction makes it smaller.
# Answer:
Enlargement

### Part (d)
# Explanation:
## Step1: Determine side lengths
Assume original figure length is 4 (grid units) and Scale Drawing B length is 8 (grid units).
## Step2: Calculate scale factor
Scale factor $ k = \frac{\text{Length of Scale Drawing B}}{\text{Length of Original Figure}}=\frac{8}{4}=2 $.
# Answer:
$ 2 $

### Part (e)
# Explanation:
## Step1: Relate scale factors
From part (b), scale factor of A to original is $ \frac{1}{2} $, so original length $ = 2a $. From part (d), scale factor of B to original is $ 2 $, so $ b = 2\times(\text{original length}) $. Substitute original length $ = 2a $ into $ b $'s formula: $ b = 2\times(2a)=4a $? Wait, no—wait, let's re - express. Let original length be $ L $. Then $ a=\frac{1}{2}L $ (so $ L = 2a $), and $ b = 2L $. Substitute $ L = 2a $ into $ b = 2L $, we get $ b=2\times(2a)=4a $? Wait, maybe better to find the scale factor from A to B. From A to original: scale factor $ \frac{1}{2} $ (A is $ \frac{1}{2} $ of original). From original to B: scale factor $ 2 $ (B is $ 2 $ times original). So from A to B: $ \frac{\text{Scale factor of B to original}}{\text{Scale factor of A to original}}=\frac{2}{\frac{1}{2}} = 4 $? Wait, no. Let's take actual lengths. Suppose A has length 2, original has length 4, B has length 8. Then from A (length 2) to B (length 8), the scale factor is $ \frac{8}{2}=4 $. So $ b = 4a $.
## Step2: Formulate the equation
If $ a $ is length in A and $ b $ is length in B, then $ b = 4a $.
# Answer:
$ b = 4a $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Part (a)

Step1: Compare sizes

Step1: Determine side lengths

Step2: Calculate scale factor

Step1: Compare sizes

Answer:

Part (b)