Question

Activity 3: Analyzing
Photographs are often cropped so that only part of the photograph
remains. Th en, this cropped portion can be reduced or enlarged.
Choose a photograph in a textbook. Place a piece of paper over the
photograph, trace its original size, and draw a rectangle to indicate
a portion of the photograph that you would like to crop. Draw a
diagonal from the lower left corner to the upper right corner of the
rectangular cropped area.

Answer 1

Activity 3: Analyzing
Photographs are often cropped so that only part of the photograph
remains. Th en, this cropped portion can be reduced or enlarged.
Choose a photograph in a textbook. Place a piece of paper over the
photograph, trace its original size, and draw a rectangle to indicate
a portion of the photograph that you would like to crop. Draw a
diagonal from the lower left corner to the upper right corner of the
rectangular cropped area. If this diagonal is extended through the
upper right corner of the cropped area, and a point selected anywhere along the
diagonal or its extension, then the rectangle having the chosen point as its upper
right corner (and the same lower left corner as the original cropped area) will have
dimensions that are proportional to the dimensions of the cropped area.
• Measure the dimensions and the length of the diagonal of the cropped area.
• Write the first four terms of an arithmetic sequence that has the length of the
diagonal of the cropped area as its first term. Using the terms of your sequence
as diagonal lengths, find the four corresponding photo widths. What do you
notice about this list of widths?
• Write the first four terms of an geometric sequence that has the length of the
diagonal of the cropped area as its first term. Using the terms of your sequence
as diagonal lengths, find the four corresponding photo widths. What do you
notice about this list of widths?