Let's start by graphing a random polygon with vertices in A(-7,- 4), B(-4,- 3), and C(-3,- 6).
A similarity transformation is a dilation or a composition of rigid motions and dilations. According to the exercise we are supposed to graph a second polygon by doing a translation and a dilation. Let's start by translating the polygon 7 units to the right and 4 steps up. This places A' at the origin which makes the dilation a bit easier.
Next, we will perform a dilation using an arbitrary scale factor of 2.
Point
(a,b)
(2a,2b)
A'
(0,0)
(0,0)
B'
(3,1)
(6,2)
C'
(4,- 2)
(8,- 4)
Let's draw the image of â–ł A''B''C''
Before we are done, we will have to remove the unnecessary parts.
To map â–ł A''B''C'' onto â–ł ABC we have to undo the similarity transformation that mapped â–ł ABC onto â–ł A''B''C''. To undo a dilation with a scale factor of 2, we have to use a scale factor of 0.5 as this brings the vertices of â–ł A''B''C'' back onto the vertices of â–ł A'B'C'. We also have to undo the translation of 7 units to the right and 4 units up. We can do that by performing a translation of 7 units to the left and 4 units down.
Dilation:& (x,y) → (1/2x,1/2y)
Translation:& (x,y) → (x-7,y-4)
