Question

Marissa has determined that there is a 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.

For both the picture and the mat, determine the ratios of the perimeter of the scaled image to the perimeter of the original item.
For both the picture and the mat, determine the ratios of the area of the scaled image to the area of the original item.

Answer 1

Explanation:

When dilation takes place, new perimeter would be equal to

old perimeter*scale factor

But New area = Old area(scale factor)^2

This is because area has units square as units

Hence when scale factor is 2,

for perimeter scale factor is 2

Hence when scale factor is 3,

for perimeter scale factor is 3

But for area,

when scale factor is 2,

for area scale factor is 4

when scale factor is 2,

for area scale factor is 9

Answer 2

Perimeter Ratio for scale factor 2: (picture)1:2 (mat)1:2

Ratio for scale factor 3: (pic) 1:3 (mat) 1:3

Ratio for scale factor 4: (pic) 1:4 (mat) 1:4

Area Ratio for scale factor 2: (pic &mat) 1:4

Ratio for scale factor 3:(pic&mat) 1:9

Ratio for scale factor 4:(pic&mat)1:16