Question 957551: kylee is using her laptop to collect some images for a project.she has one rectangular image that measures 4.8cm by 6.2cm.kylee then enlarges the image so it now measures 16.8cm by 21.7cm.
(a) what is the scale factor of this enlargement (i think it is 3.5 )
Later kylee finds the image is now too big.she clicks the mouse to reduce the image to 7.2cm by 9.3cm.
(b) what is the scale factor of this reduction of the enlarged image used in part (a)
(c) overall,has the image been enlarged or reduced?find the scale factor for this overall change.
(d) if the original image changes from 4.8cm to 10.2cm,but the width remains the same as before,does this make it a true enlargement of the original image.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! she starts at 4.8 by 6.2 and it now measures 16.8 by 21.7
the vertical to horizontal ratio is 4.8 / 6.2 = .7741935484
the vertical scale factor is 16.8 / 4.8 = 3.5
the horizontal scale factor is 21.7 / 6.2 = 3.5
since both scale factors are the same, the enlarged image has the same proportions as the original image.
the vertical to horizontal ratio is 16.8 / 21.7 = .7741935484
she reduces the image to 7.2 by 9.3
the vertical scale factor is 7.2 / 16.8 = .4285714286
the horizontal scale factor is 9.3 / 21.7 = .4285714286
since both scale factors are the same, the reduced image has the same proportions as the original image and the enlarged image.
the vertical to horizontal ratio is 7.2 / 9.3 = .7741935484
the original image is 4.8 by 6.2
the final image is 7.2 by 9.3
the overall change in the size of the image is an enlargement.
the overall scale factor is:
vertical from 4.8 to 7.2 = scale factor of 1.5
horizontal from 6.2 to 9.3 = scale factor of 1.5
the scale factor for vertical and horizontal is the same so the image is still in proportion.
the original image is 4.8 by 6.2
the modified image is 10.2 by 6.2
the vertical scale factor is 10.2 / 4.8 = 2.125
the horizontal scale factor is 6.2 / 6.2 = 1
the resulting picture will not be a true enlargement because the picture is not in proportion any longer.
a true enlargement only changes the size.
it doesn't change any of the relationships between the parts.
that's my understanding.
the two figures are geometrically similar if they are proportional.
that means the size is changed but not the shape.
the last example changes the shape so it is not a true enlargeement.
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