Given:
The preimage and image of a triangle in the given figure.
To find:
The dilation scale factor.
Solution:
From the given figure it is clear that the vertices of the triangle ABC are A(-2,-2), B(-1,2) and C(2,1).
The vertices of the triangle A'B'C' are A'(-4,-4), B'(-2,4) and C'(4,2).
If a figure is dilated by factor K with (0,0) as the center of dilation, then
[tex](x,y)\to (kx,ky)[/tex]
Let the scale factor be K, then the image of point A is:
[tex]A(-2,-2)\to A'(k(-2),k(-2))[/tex]
[tex]A(-2,-2)\to A'(-2k,-2k)[/tex]
From the given figure it is clear that the image of point A is A'(-4,-4).
[tex]A'(-2k,-2k)=A'(-4,-4)[/tex]
On comparing both sides, we get
[tex]-2k=-4[/tex]
[tex]k=\dfrac{-4}{-2}[/tex]
[tex]k=2[/tex]
Therefore, the dilation scale factor is 2.
