Question

Please help, determine whether the image was enlarged or reduced and by what scale factor

Answer 1

Image was reduced by a scale factor =
`(1)/(2)`

Explanation:

Since, segment A'B' is the image of segment AB,

Scale factor =
`\frac{\text{Length of image}}{\text{Length of actual}}`

=
`(A'B')/(AB)`

Length of AB =
`√((BB')^2+(AB')^2)` [By Pythagoras theorem]

=
`√(2^2+4^2)`

=
`√(20)`

=
`2√(5)`

Length of A'B' =
`√(1^2+2^2)`

=
`√(5)`

Scale factor =
`(√(5) )/(2√(5) )`

=
`(1)/(2)`

Therefore, image AB has been reduced by a scale factor of
`(1)/(2)`