Dilations and Scale Factors

If a figure is dilated by a scale factor of 1/2, what happens to its size?

• It doubles in size.

• It is reduced to half its size.

• It remains the same size.

• It triples in size.

Answer explanation

A scale factor of 1/2 means each dimension of the figure is multiplied by 1/2, resulting in a size that is half of the original. Therefore, the correct answer is that it is reduced to half its size.

A rectangle with dimensions 4 cm by 6 cm is dilated by a scale factor of 2. What are the dimensions of the new rectangle?

• 8 cm by 12 cm

• 6 cm by 8 cm

• 2 cm by 3 cm

• 12 cm by 24 cm

Answer explanation

To find the dimensions of the new rectangle after dilation, multiply each original dimension by the scale factor of 2. Thus, 4 cm becomes 8 cm and 6 cm becomes 12 cm, resulting in dimensions of 8 cm by 12 cm.

What is the scale factor if a line segment measuring 8 units is dilated to 20 units?

• 2.5

• 0.4

• 4

• 1.25

Answer explanation

To find the scale factor, divide the new length by the original length: 20 units ÷ 8 units = 2.5. Thus, the scale factor is 2.5.

A dilation with a scale factor of 1 produces what kind of image?

• An image that is smaller than the original

• An image that is larger than the original

• An image that is congruent to the original

• An image that disappears

Answer explanation

A dilation with a scale factor of 1 means the image remains the same size as the original. Therefore, the resulting image is congruent to the original.

What happens to the area of a figure when it is dilated by a scale factor k?

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Answer explanation

When a figure is dilated by a scale factor k, its area is multiplied by k². This means if the scale factor is 2, the area becomes 4 times larger; if it's 0.5, the area becomes 0.25 times smaller.

Calculating Scale Factor: A rectangle is dilated, and the dimensions change from 5 cm by 8 cm to 15 cm by 24 cm. Calculate the scale factor.

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Answer explanation

To find the scale factor, divide the new dimensions by the original dimensions. For width: 15 cm / 5 cm = 3. For height: 24 cm / 8 cm = 3. The scale factor is 3.

Finding Missing Dimensions: A triangle is dilated by a scale factor of 0.5. One side of the pre-image measures 12 cm. What is the length of the corresponding side in the image?

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Answer explanation

To find the length of the corresponding side in the image, multiply the pre-image side (12 cm) by the scale factor (0.5). Thus, 12 cm * 0.5 = 6 cm. The length of the corresponding side in the image is 6 cm.

A square with side length 4 cm is dilated by a scale factor of 1.5. What is the side length of the new square?

• 10 cm

• 8 cm

• 4 cm

• 6 cm

Dilate Point A by a scale factor of 1/2

• (-4,-4)

• (-1,-4)

• (-1,-1)

• (-2,-2)

Does the image show a Dilation?

• Yes

• No