Question

a dilation centered at the origin maps the point (1,3) to the point (4,12). what is the scale factor of the dilation?

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin, the transformation of a point \((x,y)\) is \((kx,ky)\), where \(k\) is the scale factor.

Step2: Apply to given points

Given original point \((1,3)\) and image point \((4,12)\). For the \(x\)-coordinate: \(1\times k = 4\), so \(k=\frac{4}{1}=4\). Check with \(y\)-coordinate: \(3\times k = 12\), so \(k=\frac{12}{3}=4\).

Answer:

4