Scale factor 1.25 is an expansion since we 'enlarge' the original size 1.25 times
Scale factor 3 is an expansion since we 'enlarge' the original size by 3 times
Scale factor -2 is also an expansion since we 'enlarge' the original size by 2 times but on the opposite direction of the centre of enlargement
Scale factor 3/4 is a contraction since we make the original size 'smaller' by 0.75 times
Scale factor 1/5 is also a contraction since we make the original size 'smaller' by 0.20 times
Literally, contraction means to reduce; while expansion means to increase.
The following absolute value inequalities are used to determine if a scale factor (k) is an expansion or a contraction.
So, we have:
The absolute value of 1.25, -2 and 3 are greater than 1. i.e.
[tex]|1.25| > 1[/tex]
Remove absolute brackets
[tex]1.25 > 1[/tex]
[tex]|-2| > 1[/tex]
Remove absolute brackets
[tex]2 > 1[/tex]
[tex]|3| > 1[/tex]
Remove absolute brackets
[tex]3 > 1[/tex]
Hence, 1.25, -2 and 3 are all expansion scale ratios
The absolute value of 3/4 and 1/5 are between 0 and 1. i.e.
[tex]0 > |3/4| > 1[/tex]
[tex]0 > |0.75 | > 1[/tex]
Remove absolute brackets
[tex]0 > 0.75 > 1[/tex]
[tex]0 > |1/5| > 1[/tex]
[tex]0 > |0.2| > 1[/tex]
Remove absolute brackets
[tex]0 > 0.2 > 1[/tex]
Hence, 3/4 and 1/5 are all contraction scale ratios
Read more about scale ratios at:
https://brainly.com/question/16713785
