Question

what is the rule for the dilation shown below?*(x,y)->(3x,3y)(x,y)->(x + 3,y + 3)(x,y)->(1/3x,1/3y)(x,y)->(x - 3,y - 3)

Explanation:

Step1: Identify coordinates of a point

Take point \( B(-6,6) \) and its image \( B'(-2,2) \).

Step2: Calculate the scale factor for \( x \)-coordinate

Scale factor \( k_x=\frac{-2}{-6}=\frac{1}{3} \).

Step3: Calculate the scale factor for \( y \)-coordinate

Scale factor \( k_y=\frac{2}{6}=\frac{1}{3} \).

Answer:

\((x,y)\to(\frac{1}{3}x,\frac{1}{3}y)\) (the third option)