Scale Factor And Dilations

1.

Gwen had a painting that had a length of 5 feet and a width of 3.5 feet. If a reproduced copy of that painting had a scale factor of 3.5,what are the new dimensions ?

A.

15 feet by 12.25 feet
B.

17.5 feet by 12.25 feet
C.

17.5 feet by 15 feet
D.

17.5 feet by 12 feet

Correct Answer
B. 17.5 feet by 12.25 feet

Explanation
The new dimensions of the reproduced copy of the painting can be found by multiplying the original dimensions by the scale factor. The original length of 5 feet multiplied by the scale factor of 3.5 gives us 17.5 feet. Similarly, the original width of 3.5 feet multiplied by the scale factor of 3.5 gives us 12.25 feet. Therefore, the new dimensions of the reproduced copy are 17.5 feet by 12.25 feet.

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2.

Under a dilation, triangle A(-1,1), B(-4,3), C(-3,4) becomes triangle M(-3/4,3/4), N(-3, 2 1/4), Q(-2 1/4,3). What is the scale factor for this dilation?

A.

1/4
B.

1/2
C.

3/4
D.

3

Correct Answer
C. 3/4

Explanation
The scale factor for a dilation is determined by comparing the corresponding side lengths of the original figure and the image after dilation. In this case, we can compare the side lengths of triangle ABC and triangle MNQ.

The length of side AB is sqrt((3-1)^2 + (-4+1)^2) = sqrt(5)
The length of side MN is sqrt((3/4+3)^2 + (3/4-2 1/4)^2) = sqrt(5)

The length of side BC is sqrt((4-3)^2 + (-3+4)^2) = sqrt(2)
The length of side NQ is sqrt((3/4+2 1/4)^2 + (3-3)^2) = sqrt(2)

The length of side AC is sqrt((4-1)^2 + (-3+1)^2) = sqrt(13)
The length of side MQ is sqrt((3/4+2 1/4)^2 + (3/4-3)^2) = sqrt(13)

Comparing the side lengths, we can see that the corresponding side lengths of triangle ABC and triangle MNQ are all multiplied by 3/4. Therefore, the scale factor for this dilation is 3/4.

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3.

A figure dilated by a scale factor of .75 would be considered an enlargement.

A.

True
B.

False

Correct Answer
B. False

Explanation
A figure dilated by a scale factor of 0.75 would actually be considered a reduction, not an enlargement. When the scale factor is less than 1, it means that the figure is shrinking or getting smaller in size. Therefore, the correct answer is False.

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4.

If a quadrilateral was reduced to 66 2/3%. What was the scale factor?

A.

2/3
B.

1/3
C.

3
D.

2

Correct Answer
A. 2/3

Explanation
The scale factor represents the ratio of the new size of an object to its original size. In this case, if a quadrilateral was reduced to 66 2/3% of its original size, it means that it was reduced to 2/3 of its original size. Therefore, the scale factor is 2/3.

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5.

If the rectangle is dilated with a scale factor of 2.75. What are the coordinates of point C?

A.

(5,5)
B.

(10,10)
C.

(13,13)
D.

(13.75, 13.75)

Correct Answer
D. (13.75, 13.75)

Explanation
When a rectangle is dilated with a scale factor of 2.75, each coordinate of the rectangle is multiplied by the scale factor. In this case, the x-coordinate and y-coordinate of point C are both multiplied by 2.75. Therefore, the coordinates of point C after dilation would be (5 * 2.75, 5 * 2.75) which simplifies to (13.75, 13.75).

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6.

The ratio of the dilated image to the original image is the __________________?

Correct Answer
Scale Factor

Explanation
The ratio of the dilated image to the original image is known as the scale factor. The scale factor represents the amount by which the dimensions of the original image are multiplied or divided to obtain the dimensions of the dilated image. It is used to determine the relationship between the sizes of the two images and is essential in understanding the changes in size that occur during dilation.

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7.

If the scale factor is between 0 and 1, the image is a(n)___________________.

Correct Answer
reduction

Explanation
If the scale factor is between 0 and 1, it means that the image is being scaled down or made smaller. This is known as a reduction.

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