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Marissa has a photograph that measures 2 in. by 4 in. She has mounted the picture on a mat so that there is a border that measures 1 in. around the picture. The graph shows a representation of the photograph and the mat on the coordinate grid.

 

Question 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.

 

Question 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.

 Dec 18, 2018
 #1
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Question  1

 

Just double the x and y coordinates for each corner of the picture and the mat and plot these new points

 

For instance....the top rigt corner of the mat becomes (2,3) *2  = (4, 6)

And the top right corner of the picture = (1,2) * 2  =  (2, 4)

 

etc.

 

 

Question 3

 

a)  The perimeter of each new image = 2 times the perimeter of the old image

     The area of each new image =   (scale factor)^2 * area of old image = 4 times the old image

 

b)  Scale factor of 3 triples the perimeter  and the area is (3)^2 = 9 times as much

     Scale factor of 4 quadruples the perimeter and the area is (4)^2 = 16 times as much

 

 

 

 

cool cool cool

 Dec 18, 2018

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