Under a dilation, triangle XYZ where X(1, 3), Y(-2, -4), and Z(5, -2.5) becomes triangle X’Y’Z’ where X’(2.5, 7.5), Y’(-5, -10), and Z’(12.5, -6.25). What is the scale factor for this dilation?

(a) -2/5
(b) 2/5
(c) 2.5
(d) -2.5

Question

Under a dilation, triangle XYZ where X(1, 3), Y(-2, -4), and Z(5, -2.5) becomes triangle X’Y’Z’ where X’(2.5, 7.5), Y’(-5, -10), and Z’(12.5, -6.25). What is the scale factor for this dilation?

(a) -2/5
(b) 2/5
(c) 2.5
(d) -2.5

anonymous · Answer

@amistre64 @aaronq

amistre64 · Answer

does x'/x  have the same ratio as say y'/y?

anonymous · Answer

no

amistre64 · Answer

that was an odd thought ...

amistre64 · Answer

do you know what a scale factor tells us?

anonymous · Answer

yeah, how much you multiply or divide...it's a ratio basically

anonymous · Answer

actually, it is a ratio

amistre64 · Answer

X’(2.5, 7.5), Y’(-5, -10), and Z’(12.5, -6.25)
 X(  1,    3  ),  Y(-2,  -4 ),  and Z(    5,    -2.5 )

dividing the parts,  is everything equal to 2.5/1?

if so, then the center of dilation will be at the origin, if not, then we would have to determine its center to find its scale factor.

anonymous · Answer

ok

anonymous · Answer

I think it's at the origin
which would make the scale factor 2.5?

amistre64 · Answer

i believe its at the origin, and it does look like it all works out at 2.5 :)

anonymous · Answer

cool! Thanks again amistre, you're always a help
would you mind looking over one more? I think I already got the right answer, but I just want to make sure..

amistre64 · Answer

1 more ...

anonymous · Answer

11

     

    Consider line segment AB whose endpoints are (1, 4) and (4, 8).  If this segment is dilated by a scale factor of 4 centered at the origin, find the length of the new segment, A’B’.

    Answer
    		

    4
    		

    5
    		

    20
    		

    400

anonymous · Answer

I chose 20