Question

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Question 1


Lynley draws the quadrilateral on the left and then uses a scale factor to create the quadrilateral on the right. Determine the correct pairs of corresponding sides. Choose 2.

(2 points)
Responses

4 units corresponds to 5 units
4 units corresponds to 5 units

4 units corresponds to 7.5 units
4 units corresponds to 7.5 units

5 units corresponds to 7.5 units
5 units corresponds to 7.5 units

6 units corresponds to 4 units
6 units corresponds to 4 units

6 units corresponds to 5 units
6 units corresponds to 5 units

6 units corresponds to 7.5 units
6 units corresponds to 7.5 units
Question 2
Determine the scale factor she used to create the second quadrilateral.(1 point)
Responses

0.67
0.67

1.25
1.25

1.5
1.5

1.875
1.875
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Answer 1

To determine the correct pairs of corresponding sides and the scale factor, we first need to check which pairs reflect the proportional scaling in the quadrilaterals.

**Question 1: Determine the correct pairs of corresponding sides. Choose 2.**

1. Let's check the provided pairs:
- **4 units corresponds to 5 units**
- **4 units corresponds to 7.5 units**
- **5 units corresponds to 7.5 units**
- **6 units corresponds to 4 units**
- **6 units corresponds to 5 units**
- **6 units corresponds to 7.5 units**

To choose the correct pairs, we need to know what the scale factor is (which will help identify corresponding sides). Let's focus on a few pairs for a moment.

To find valid pairs, check if the ratio of the lengths from the original quadrilateral to the new quadrilateral holds true:
- If we denote the original length as 'a' and the scaled length as 'b', then a:b should equal the same constant for all sides if the quadrilateral is a scaled version.

2. Let's assume a scale factor of 1.25 as an example since it relates to 5 being 1.25 times 4:
- If the original side is 4 units (or 5 units),
- Scaling by 1.25:
- 4 units * 1.25 = 5 units
- 5 units * 1.25 = 6.25 units (but we don't have this option)

Given that we have:
- 4:5 (1.25)
- 4:7.5 (1.875)
- 5:7.5 (which does not give a clear answer)
- 6:4 (which does not correspond to a scale factor > 1)

The better fitting ratio is:
- **4 units corresponds to 5 units**
- **5 units corresponds to 7.5 units**

3. For the final selection:
- **The two correct pairs likely are**:
- 4 units corresponds to 5 units
- 5 units corresponds to 7.5 units

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**Question 2: Determine the scale factor she used to create the second quadrilateral.**

Since we observe that:
- 4 units scales to 5 units (scale factor of 1.25)
- 5 units scales to 7.5 units has a factor of 1.5 (7.5/5 = 1.5)

The scale factors seem to change depending on which side you're looking at. However, since the first concerning pair leads us to a probable conclusion that **the scale factor used in the first part was 1.25** but since that's not an option, it looks like the overall scale from 5 to 7.5 confirms that **1.5 is a valid uniform scale factor across sides**.

Thus, the final response for question two will be:
- **1.5**