Question

use the image to answer the question

determine whether the dilation, with a center at the origin, is an enlargement or a reduction

Explanation:

Step1: Find the coordinates of points

Let's assume the coordinate of \(A\) is \((-2,0.5)\) and the coordinate of \(A'\) is \((-4,1)\).

Step2: Calculate the scale factor

The scale factor \(k\) for a dilation centered at the origin is given by \(k=\frac{x_{A'}}{x_{A}}=\frac{y_{A'}}{y_{A}}\).
For \(x\) - coordinates: \(k=\frac{- 4}{-2}=2\).
For \(y\) - coordinates: \(k = \frac{1}{0.5}=2\).

Answer:

Since the scale factor \(k = 2>1\), the dilation is an enlargement.