Step 1: Define dilation
To dilate a figure in the coordinate plane, multiply the coordinate of each vertex by the scale factor, k. This is called mapping. For any dilation the mapping will be (x,y)→(kx,ky) . The center of dilation will always be the origin unless otherwise stated or given
Step 2: Write out the coordinates of the vertices of the Rhombus
[tex]W(2,-4),X(6,-2),Y(10,-4),Z(6,-6)[/tex]
Step 2: Write out the mapping for dilation with constant k = 3/2 = 1.5
The mapping, D, is defined as
[tex]D\colon(x,y)\to(1.5x,1.5y)[/tex]
Step 3: Find the coordinates of W', X', Y', Z'
[tex]\text{Coordinates of W' }=(1.5(2),1.5(-4))=(3,-6)[/tex]
[tex]\text{Coordinates of X' }=(1.5(6),1.5(-2))=(9,-3)[/tex]
[tex]\text{Coordinates of Y' }=(1.5(10),1.5(-4))=(15,-6)[/tex]
[tex]\text{Coordinates of Z' }=(1.5(6),1.5(-6))=(9,-9)[/tex]
Hence, the coordinates of the vertices Rhombus after dilation are:
W'(3, -6)
X'(9, -3)
Y'(15, -6)
Z'(9, -9)
