Mathematics
Grade-8
Easy

Question

Find the value of the variable m and n for the following figure that undergoes a dilation.

  1. m = 16, n = 20
  2. m = 20, n = 16
  3. m = 4, n = 8
  4. m = 4, n = 5

The correct answer is: m = 16, n = 20


    When a figure undergoes dilation, it has a scale factor. Scale factor is the ratio of a length in the image to the corresponding length in the preimage is scale factor.
    14 over 7 equals m over 8 equals n over 10
s o space 14 over 7 equals m over 8
space space space 2 space equals m over 8
m equals 16 space
14 over 7 equals n over 10
2 equals n over 10
n space equals 20 space
s o space t h e space a n s w e r space i s space colon space n equals 20 comma space a n d space m equals 16
space

    Scale factor : Scale Factor is defined as the ratio of the size of the new image to the size of the old image
    • If the scale factor is greater than 1, the image is an enlargement. It expands.
    • If the scale factor is between 0 and 1, the image is a reduction. It contracts.
    • If the scale factor is 1, the figure and the image are the exact same size (congruent).

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