Question

5. Reflection: Marissa wants to describe the relationship between the scale factor and perimeter of an image and its pre-image and between the scale factor and area of an image and its pre-image. What should she say about the relationship between the scale factor and perimeter of an image and its pre-image? What should she say about the relationship between the scale factor and area of an image and its pre-image? Support her statements using scale factors of 5 and 6.

Answer 1

Relationship between the scale factor and perimeter of an image and its pre-image?

Scale factor = k

Pre-image lengths: a, b => perimeter = 2a + 2b

Image lenghts: ka, kb => perimeter = 2ka + 2 kb = k (2a + 2b) = 2 * preimage permeter.

=> She has to say that the perimeter of the image is the perimeter of the preimage times the same scale factor.

What should she say about the relationship between the scale factor and area of an image and its pre-image?

area of the pre-image = ab

are of the image = (ka)(kb) = k^2 (ab)

=> The area of the image is the area of the preimage times the square of the scale factor.

 Support her statements using scale factors of 5 and 6.

Scale factor 5

length of the pre-image = 3 x 4 => perimeter = 2 (3 + 4) = 2(7) = 14

length of the image = 3*5 x 4*5 = 15 x 20 => perimeter = 2 (15 + 20) = 2 (35) = 70

=> 14 * 5 = 70 which shows the prediction

area of the pre-image = 3 * 4 = 12

area of the image = 15 * 20 = 300

12 * (5^2) = 12*25 = 300 which is the value predicted.

Now you can do the same using scale factor 6.