Question

polygon abcd is dilated about the origin, o, to create polygon abcd. point a is located at (1, 3), and point a is located at (4, 12). which type of dilation was used to create polygon abcd, and what is the scale factor? the polygon was enlarged by a scale factor of \\( \frac { 1 } { 4 } \\). the polygon was reduced by a scale factor of \\( \frac { 1 } { 4 } \\). the polygon was enlarged by a scale factor of 4. the polygon was reduced by a scale factor of 4.

Explanation:

Step1: Calculate the scale factor for \(x\) - coordinate

The formula for scale factor \(k\) is \(k=\frac{x_{A'}}{x_{A}}\). Given \(x_{A} = 1\) and \(x_{A'}=4\), then \(k=\frac{4}{1}=4\).

Step2: Calculate the scale factor for \(y\) - coordinate

The formula for scale factor \(k\) is \(k = \frac{y_{A'}}{y_{A}}\). Given \(y_{A}=3\) and \(y_{A'}=12\), then \(k=\frac{12}{3}=4\).
Since the scale factor \(k = 4>1\), the polygon is enlarged.

Answer:

The polygon was enlarged by a scale factor of \(4\).