Dilation and Scale Factors Quiz

A triangle is dilated by a scale factor of 3. If the original side length is 5 units, what is the side length of the dilated triangle?

• 15 units

• 8 units

• 10 units

• 5 units

Answer explanation

To find the side length of the dilated triangle, multiply the original side length (5 units) by the scale factor (3). Thus, 5 units x 3 = 15 units, making the correct answer 15 units.

Tags

CCSS.8.G.A.3

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.

Tags

CCSS.8.G.A.3

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.

Tags

CCSS.8.G.A.3

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.

Tags

CCSS.8.G.A.3

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.

Tags

CCSS.8.G.A.3

A dilation with a scale factor less than 1 results in an enlargement.

• True

• False

Answer explanation

A dilation with a scale factor less than 1 results in a reduction, not an enlargement. Therefore, the statement is false.

Tags

CCSS.8.G.A.3

Dilations preserve the shape and angles of the original figure.

• True

• False

Answer explanation

True. Dilations maintain the shape and angles of the original figure, meaning that while the size may change, the proportions and angles remain consistent.

Tags

CCSS.8.G.A.3

If the scale factor is 3, every length in the image is three times the corresponding length in the pre-image.

• True

• False

Answer explanation

True. A scale factor of 3 means that every length in the image is indeed three times the corresponding length in the pre-image, confirming the statement.

Tags

CCSS.8.G.A.3

A dilation centered at the origin always keeps the image on the same side of the coordinate plane as the pre-image.

• True

• False

Answer explanation

True. A dilation centered at the origin scales distances from the origin, maintaining the relative position of points. Thus, the image remains on the same side of the coordinate plane as the pre-image.

Tags

CCSS.8.G.A.3

The scale factor can be negative.

• True

• False

Answer explanation

The scale factor represents a ratio of sizes. It must be positive to maintain the orientation and size of the object. Therefore, the statement that the scale factor can be negative is false.

Tags

CCSS.7.G.A.1