Question

Find the dimensions of the reduction. To place a picture in his class newsletter, Joaquin must reduce the picture by a scale factor of 0.3 . Find the dimensions of the reduced picture if the origin is 15 centimeters wide and 10 centimeters high.

Vectors and spaces
ANSWERED
asked 2020-11-30
Find the dimensions of the reduction.
To place a picture in his class newsletter, Joaquin must reduce the picture by a scale factor of 0.3 . Find the dimensions of the reduced picture if the origin is 15 centimeters wide and 10 centimeters high.

Answers (1)

2020-12-01
A scale factor is the ratio of the dilated image's dimension and the original image's corresponding dimension. A scale factor then tells you what you need to multiply the dimensions of the original image by to get the dimensions of the dilated image.
A scale factor of 0.3 then means the dimensions of the reduced picture are 0.3 times the dimensions of the original picture.
The original picture has a width of 15 cm so if the reduced picture has a width that is 0.3 times the width of the original picture, then the reduced picture has a width of \(\displaystyle{0.3}{\left({15}\right)}={4.50}{.3}{\left({15}\right)}={4.5}{c}{m}.\)
The original picture has a height of 10 cm so if the reduced picture has a height that is 0.3 times the height of the original picture, then the reduced picture has a height of \(\displaystyle{0.3}{\left({10}\right)}={30.3}{\left({10}\right)}={3}{c}{m}.\)
The dimensions of the reduced picture are then 4.5 cm wide and 3 cm high 4.5 cm wide and 3 cm high
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