Understanding Scale Factors and Dilation

Mr. Holcomb presents a lesson on the fundamental theorem of similarity, focusing on determining scale factors and locating the center of dilation. The video includes exercises to apply these concepts, with detailed explanations and verifications of measurements. The lesson concludes with exercises exploring scale factors greater and less than one.

What is the scale factor if the length of the image is 10 cm and the preimage is 5 cm?

• 5

• 0.5

• 2

• 1

How do you determine the center of dilation?

• By finding the intersection of lines through corresponding points

• By measuring the distance between image and preimage

• By calculating the average of image and preimage lengths

• By using a protractor

If the scale factor is 2, what should be the length of the image if the preimage is 36 mm?

• 18 mm

• 72 mm

• 36 mm

• 54 mm

What is the relationship between the image and preimage in terms of scale factor?

• Image is always smaller than preimage

• Image is always larger than preimage

• Image is the scale factor times the preimage

• Image is equal to preimage

How do you verify the scale factor using measurements?

• By using a compass

• By counting the number of sides

• By measuring the lengths and checking the ratio

• By comparing the areas of image and preimage

How can you find the location of a point after dilation with a scale factor of 4?

• By subtracting 4 from each coordinate

• By dividing the coordinates by 4

• By multiplying the coordinates by 4

• By adding 4 to each coordinate

What is the result of multiplying a length by a scale factor of 4?

• The length remains the same

• The length is divided by 4

• The length is multiplied by 4

• The length is reduced by 4

What happens to a figure when it is dilated with a scale factor less than 1?

• It becomes larger

• It becomes smaller

• It changes shape

• It remains the same size

If a point is at (12, 8) and is dilated by a scale factor of 5/12, what is the new x-coordinate?

• 5

• 10

• 12

• 8

What is the effect of a scale factor of 1 on a figure?

• The figure is enlarged

• The figure is inverted

• The figure is reduced

• The figure remains unchanged