Dilation & Scale Factors

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

Tags

CCSS.8.G.A.3

Dilate Point A by a scale factor of 1/2

• (-4,-4)

• (-1,-4)

• (-1,-1)

• (-2,-2)

Tags

CCSS.8.G.A.3

Does the image show a Dilation?

• Yes

• No

Tags

CCSS.HSG.CO.A.2

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.7.G.A.1

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

Explain how to calculate the scale factor given the lengths of a side in the pre-image and the image.

Answer explanation

To calculate the scale factor, divide the length of a side in the image by the length of the corresponding side in the pre-image. Scale Factor = Length of Image Side / Length of Pre-image Side.

Tags

CCSS.7.G.A.1

What is the scale factor from the small shape to the big shape?

• 1/2

• 7/3

• 2

• 10/3

Tags

CCSS.7.G.A.1