Question

give the coordinates after the dilation.
original coordinates → final coordinates
x(-6,9)→x(-2,3)
y(3,6)→y(1,2)
z(-9,-6)→z(-3,-2)
(b) choose the general rule below that describes the dilation mapping △xyz to △xyz.
(x,y)→(\frac{1}{3}y,\frac{1}{3}x) (x,y)→(x,\frac{1}{3}y)
(x,y)→(\frac{1}{3}x,\frac{1}{3}y) (x,y)→(\frac{1}{3}x,y)
(x,y)→(3y,3x) (x,y)→(3x,\frac{1}{3}y)
(x,y)→(3x,3y) (x,y)→(\frac{1}{3}x,3y)

Explanation:

Step1: Analyze the transformation of \(X(-6,9)\) to \(X'(-2,3)\)

For the \(x -\)coordinate: \(\frac{-2}{-6}=\frac{1}{3}\). For the \(y -\)coordinate: \(\frac{3}{9}=\frac{1}{3}\).

Step2: Analyze the transformation of \(Y(3,6)\) to \(Y'(1,2)\)

For the \(x -\)coordinate: \(\frac{1}{3}\). For the \(y -\)coordinate: \(\frac{2}{6}=\frac{1}{3}\).

Step3: Analyze the transformation of \(Z(-9,-6)\) to \(Z'(-3,-2)\)

For the \(x -\)coordinate: \(\frac{-3}{-9}=\frac{1}{3}\). For the \(y -\)coordinate: \(\frac{-2}{-6}=\frac{1}{3}\).

Answer:

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