7 of 77 of 7 Items

Question

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
Skip to navigation

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

---

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