Dilation and Scale Factors

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.

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.

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.

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

Evaluate responses using AI:

OFF

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.

How do you write the algebraic notation when the scale factor is 1/2?

• (x, y) −> (2x, 2y)

• (x, y) −> (1/2x, 1/2y)

• (x, y) −> (-2x, -2y)

• (x, y) −> (2x, 1/2y)

Choose the correct scale factor:

• 2

• 3

• 1/3

• 1/2

Describe the similarity transformation that maps to (dilations have a center at the origin).

• a dilation with a scale factor of 2 followed by a translation 4 units right and 3 units down.

• a dilation with a scale factor of 1 / 2 followed by a translation 4 units left and 3 units up.

• Translation 4 units right and 3 units down followed by a dilation with a scale factor 2.

• Translation 4 units left and 3 units up followed by a dilation with a scale factor 1 / 2.

If the scale factor is less than one, the new figure will be

• an enlargement

• a reduction

• a scale factor

• bigger

If the scale factor is greater than one, the new figure will be

• reduction

• enlargement

• scale

• not proportional

Which of the following is the algebraic representation for a dilation?

• (x, y) → (x, 3y)

• (x, y) → (3x, 3y)

• (x, y) → (x, y - 3)

• (x, y) → (.5x, .4y)