Question

what is the rule for the transformation from the smaller polygon to the larger polygon? assume all dilations are centered at the origin
a. ( f(x,y)=(3x,3y) )
b. ( f(x,y)=(2x,2y) )
c. ( f(x,y)=(\frac{1}{2}x,\frac{1}{2}y) )
d. ( f(x,y)=(\frac{1}{3}x,\frac{1}{3}y) )

Explanation:

Step1: Find the scale factor for \(x\) - coordinate

Take a point on the smaller polygon, say \((3,1)\). On the larger polygon, the corresponding point (after dilation) is \((9,3)\).
The scale factor \(k_x=\frac{9}{3}=3\)

Step2: Find the scale factor for \(y\) - coordinate

Using the same points \((3,1)\) and \((9,3)\), the scale factor \(k_y = \frac{3}{1}=3\)

Since the dilation is centered at the origin, the rule for dilation is \(f(x,y)=(kx,ky)\) where \(k = 3\)

Answer:

A. \(f(x,y)=(3x,3y)\)