Question

2.1 triangle abc is dilated by a scale factor of 3. the image is triangle abc
side length ab = 10 mm m∠abc = 21°
answer the following:
side length ab = 45 m∠abc = 20.25
3.1 quadrilateral abce is dilated to get quadrilateral abce using center f.
what is the scale factor of dilation? show your calculations

Explanation:

Step1: Recall the property of dilation

Dilation is a transformation that changes the size of a figure but not its shape. For a dilation with center \(F\), if a segment \(AB\) is dilated to \(A'B'\), the scale factor \(k\) is given by the ratio of the length of the image segment to the length of the original segment (\(k=\frac{A'B'}{AB}\)) or vice - versa. Also, the measure of angles in a dilated figure is the same as the measure of angles in the original figure because dilation is a similarity transformation.

Step2: Calculate the scale factor for the quadrilateral dilation

Let's assume the original side length (from the smaller quadrilateral) and the image side length (from the larger quadrilateral). If we consider the ratio of the side lengths. Let the original side length be \(x = 1.5\) and the image side length be \(y=3\). The scale factor \(k\) of dilation is \(k=\frac{y}{x}\).

$$k=\frac{3}{1.5}=2$$

Answer:

The scale factor of dilation is \(2\).