Question

if the origin is the center of this dilation, choose the correct scale factor: 1/3 3 1/2 2

Explanation:

Step1: Determine the length of a corresponding side in the original and dilated figure

Let's assume the length of a side in the smaller figure (pre - image) is \(1\) unit (for example, if we consider the vertical or horizontal side of the smaller square - like part near the origin). The length of the corresponding side in the larger figure (image) is \(3\) units.

Step2: Use the scale factor formula

The scale factor \(k\) of a dilation with center at the origin is given by \(k=\frac{\text{length of a side in the image}}{\text{length of the corresponding side in the pre - image}}\). But since the smaller figure is the pre - image and the larger is the image, if we reverse the perspective (assuming the problem is about the dilation from the smaller to the larger), we can also use the ratio of coordinates. Let's take a point \(P\) in the pre - image. Suppose a point \(P(x,y)\) in the pre - image and its image \(P'(x',y')\) after dilation. If the center of dilation is the origin \((0,0)\), then \(x' = kx\) and \(y'=ky\). If we assume a point in the smaller figure (pre - image) has coordinates \((1,1)\) (for simplicity, considering a non - origin point on the figure) and the corresponding point in the larger figure (image) has coordinates \((3,3)\) (by visual inspection of the grid - like structure in the graph), then \(k = 3\)

Answer:

3