Question

question
what is the image of $(6,12)$ after a dilation by a scale factor of $\frac{1}{2}$ centered at the origin?
answer attempt 1 out of 2

Explanation:

Step1: Apply dilation formula

For a point \((x,y)\) dilated by scale factor \(k\) centered at origin, new point is \((kx,ky)\). Here \(x = 6\), \(y=12\), \(k=\frac{1}{2}\).

Step2: Calculate new \(x\)-coordinate

\(x_{new}=\frac{1}{2}\times6 = 3\)

Step3: Calculate new \(y\)-coordinate

\(y_{new}=\frac{1}{2}\times12 = 6\)

Answer:

\((3,6)\)