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?

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.

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?

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