Question

question what is the image of (0, 6) after a dilation by a scale factor of $\frac{1}{3}$ centered at the origin? answer

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor \(k\), if the original point is \((x,y)\), the image point \((x',y')\) is given by \((x',y')=(kx,ky)\).

Step2: Identify values of \(x\), \(y\), and \(k\)

Here, \(x = 0\), \(y = 6\), and \(k=\frac{1}{3}\).

Step3: Calculate \(x'\)

\(x'=k\times x=\frac{1}{3}\times0 = 0\)

Step4: Calculate \(y'\)

\(y'=k\times y=\frac{1}{3}\times6 = 2\)

Answer:

\((0,2)\)