Dilation and Scale Factors

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.

Evaluate responses using AI:

OFF

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.

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.

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.

In the figure above, a dilation from A to A' has occurred. What is the scale factor?

Mathematical Equivalence

ON

Match the following to show a dilation by a scale factor k=5.

• (-5,5)

• (3, -2)

• (5,0)

• (0, -1)

• (15,-10)

• (-1, 1)

• (0,-5)

• (1, 0)

• (10,15)

• (2, 3)

In the figure above, a dilation from A to A' has occurred. What is the scale factor?

Mathematical Equivalence

ON

Segment CD is dilated from point O by a scale factor of 4. Where are C' and D' located?

(Choose TWO points, one for C and one for D.)

When a dilation has a scale factor greater than one, the dilation is an (a)   .

• enlargement

• reduction

Find the measure of x:

• 6

• 24

• 33

• 36