Similarity
Solve the problems. When you have finished, submit this assignment to your teacher by the due date for full credit.
1:

(2 points)
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1. Marissa has decided to dilate the picture and the mat by a scale factor of 2. Draw the new image for the picture and mat on the coordinate grid.


(6 points)
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2. Marissa labeled the corners of both the picture and the mat as shown. Complete the table.



Point Original Ordered Pair
(x, y) Ordered Pair When Scale Factor Is 2 Ordered Pair When Scale Factor Is 3 Ordered Pair When Scale Factor Is 4
A (-1,2)
B (1,2)
C (1,-2)
D (-1,-2)
E (-2,3)
F (2,3)
G (2-3)
H (-2,-3)

(4 points)
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3. Marissa thinks that there could be a pattern 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.
(a) Determine the perimeter and area of the picture and the perimeter and area of the mat.
(b) Create a table that shows the perimeter and area of the picture and the perimeter and area of the mat for scale factors of 2, 3, and 4.


Picture
Scale Factor Length Width Perimeter Area
2
3
4

Mat
Scale Factor Length Width Perimeter Area
2
3
4

(4 points)
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4. 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.
(a) For both the picture and the mat, determine the ratios of the perimeter of the scaled image to the perimeter of the original item.
(b) For both the picture and the mat, determine the ratios of the area of the scaled image to the area of the original item.



(a) Ratio of the perimeter of the scaled image to the perimeter of the original item:

Ratio for Scale Factor of 2 Ratio for Scale Factor of 3 Ratio for Scale Factor of 4
Picture 1:2 1:3 1:4
Mat

(b) Ratio of the area of the scaled image to the area of the original item:

Ratio for Scale Factor of 2 Ratio for Scale Factor of 3 Ratio for Scale Factor of 4
Picture 1:4 1:9 1:16
Mat

(4 points)
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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.