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.
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.
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.
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)
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