If the center of dilation is the origin O(0,0), the image of each vertex of the polygon can be found by multiplying their coordinates by the scale factor.
A dilation by a scale factor of 23 can be written as D_(23). Since the center of dilation is the origin O(0,0), we can find the image of each of the vertices of the quadrilateral by multiplying their coordinates by the scale factor 23. Let's do it!
ABCD
A'B'C'D'
A(3,0)
A'(3* 2/3, 0* 2/3) ⇒ A'(2, 0)
B(1,- 2)
B'(1* 2/3, -2* 2/3) ⇒ B'(2/3,-4/3)
C(3,- 5)
C'(3* 2/3, -5* 2/3) ⇒ C'(2,-10/3)
D(7,- 1)
D'(7* 2/3, -1* 2/3) ⇒ D'(14/3,-2/3)
Finally, we will plot and connect the obtained vertices to draw D_(23)( ABCD)= A' B' C' D'.
As we can see, A'(2,0), B'( 23,- 43), C'(2,- 103), and D'( 143,- 23) are the coordinates of the image.
