Ask a New Question
Menu

Question 1

A)
Use the image to answer the question.

One smaller and one larger triangle side by side.

A triangle has a base of 8 cm and a height of 3 cm. The triangle is dilated by a scale factor of 3. Calculate and compare the areas of the dilated triangle and the original triangle.

(1 point)
Responses

The original triangle has an area of 24 cm2 and the dilated triangle has an area of 108 cm2; therefore, the dilated triangle has an area 4.5 times the size of the original triangle.
The original triangle has an area of 24 cm squared and the dilated triangle has an area of 108 cm squared ; therefore, the dilated triangle has an area 4.5 times the size of the original triangle.

The original triangle has an area of 24 cm2 and the dilated triangle has an area of 36 cm2; therefore, the dilated triangle has an area 1.5 times the size of the original triangle.
The original triangle has an area of 24 cm squared and the dilated triangle has an area of 36 cm squared ; therefore, the dilated triangle has an area 1.5 times the size of the original triangle.

The original triangle has an area of 12 cm2 and the dilated triangle has an area of 108 cm2; therefore, the dilated triangle has an area 9 times the size of the original triangle.
The original triangle has an area of 12 cm squared and the dilated triangle has an area of 108 cm squared ; therefore, the dilated triangle has an area 9 times the size of the original triangle.

The original triangle has an area of 12 cm2 and the dilated triangle has an area of 36 cm2; therefore, the dilated triangle has an area 3 times the size of the original triangle.
The original triangle has an area of 12 cm squared and the dilated triangle has an area of 36 cm squared ; therefore, the dilated triangle has an area 3 times the size of the original triangle.
Question 2
A)
Use the image to answer the question.

One smaller and one larger square side by side.

Chaz draws a square with sides equal to 4 units, then he dilates the square so the sides are equal to 6 units. Chaz writes a fraction in lowest terms to express the relationship between the area of the original square and the dilated square, with the numerator expressing the area of the dilated square. What is that fraction?

(1 point)
Responses

23
Start Fraction 2 over 3 End Fraction

49
Start Fraction 4 over 9 End Fraction

1636
16 over 36

214
2 Start Fraction 1 over 4 End Fraction
Question 3
A)Kierra draws a triangle with a base of 10 cm and a height of 15 cm. She dilates the triangle using a scale factor of 45. Then, Kierra finds the difference between the two areas by subtracting. How much greater is the area of the original triangle than the area of the dilated triangle?(1 point)
Responses

27 cm2
27 cm squared

75 cm2
75 cm squared

54 cm2
54 cm squared

48 cm2
48 cm squared
Question 4
A)Determine how dilation affects the area of a pentagon when the sides of the pentagon are dilated by a scale factor less than 1.(1 point)
Responses

The area decreases, but less rapidly than the lengths of the sides decrease.
The area decreases, but less rapidly than the lengths of the sides decrease.

The area increases, but less rapidly than the lengths of the sides increase.
The area increases, but less rapidly than the lengths of the sides increase.

The area decreases more rapidly than the lengths of the sides decrease.
The area decreases more rapidly than the lengths of the sides decrease.

The area increases more rapidly than the lengths of the sides increase.
The area increases more rapidly than the lengths of the sides increase.
Question 5
A)
Use the image to answer the question.

A triangle with unequal sides with the base labelled 6 and height labelled 4.

Mike draws a triangle and dilates it by a scale factor of 2.5. If the triangle’s original dimensions are 4 inches high and 6 inches along its base, what is the area in square inches of Mike’s dilated triangle?

(1 point)
Responses

75
75

60
60

150

1 answer

Question 1:

To calculate the area of the original triangle:

  • Area = (Base * Height) / 2
  • Area = (8 cm * 3 cm) / 2 = 24 cm²

When dilated by a scale factor of 3:

  • New base = 8 cm * 3 = 24 cm
  • New height = 3 cm * 3 = 9 cm

Area of the dilated triangle:

  • Area = (Base * Height) / 2
  • Area = (24 cm * 9 cm) / 2 = 108 cm²

Comparing areas:

  • 108 cm² (dilated) / 24 cm² (original) = 4.5 times larger

Correct response: The original triangle has an area of 24 cm² and the dilated triangle has an area of 108 cm²; therefore, the dilated triangle has an area 4.5 times the size of the original triangle.

Question 2:

To find the areas:

  • Area of the original square = 4 units * 4 units = 16 square units
  • Area of the dilated square = 6 units * 6 units = 36 square units

Fraction representing the area relationship:

  • Area of the dilated square over area of the original square = 36 / 16 = 9/4 (in lowest terms)

Correct response: None of the available responses accurately represent the fraction; however, the closest approximation in terms of numerical values would be 2 (start fraction 1 over 4 end fraction).

Question 3:

Kierra's original triangle has:

  • Area = (Base * Height) / 2 = (10 cm * 15 cm) / 2 = 75 cm²

For the dilated triangle with a scale factor of 45:

  • New base = 10 cm * 45 = 450 cm
  • New height = 15 cm * 45 = 675 cm
  • Area of the dilated triangle = (450 cm * 675 cm) / 2 = 151875 cm²

Difference between the areas:

  • Difference = 75 cm² (original) - 151875 cm² (dilated) cannot calculate as it shows dilated area is much larger.

Hence, the response must be evaluated against the original responses available since the calculations indicate Kierra made a mistake in understanding dilation complex effect on area.

Correct response: 75 cm².

Question 4:

When the sides of a pentagon are dilated by a scale factor less than 1 (meaning the pentagon shrinks):

  • The area decreases as the square of the scale factor.

Correct response: The area decreases more rapidly than the lengths of the sides decrease.

Question 5:

The original triangle has:

  • Area = (Base * Height) / 2 = (6 * 4) / 2 = 12 square inches

When dilated by a scale factor of 2.5:

  • New base = 6 inches * 2.5 = 15 inches
  • New height = 4 inches * 2.5 = 10 inches

Area of the dilated triangle:

  • Area = (15 * 10) / 2 = 75 square inches

Correct response: 75.