Question

2. Quadrilateral PQRS with P(-5, 1). Q(-2,6), R(3,7), and S(6,4); dilate by a scale factor of 4 12 a. Is this an enlargement or reduction? How do you know? 14 b. What are the vertices of the image after the transformation?

Answer 1

Answer and Explanation:

Given the vertices of the quadrilateral PQRS as P(-5, 1). Q(-2,6), R(3,7), and S(6,4), let's go ahead and dilate with a scale factor of 4 as shown below;

$P(-5,1)\rightarrow P^{\prime}(-5\times4,1\times4)\rightarrow P^{\prime}(-20,4)$$Q(-2,6)\rightarrow Q^{\prime}(-2\times4,6\times4)\rightarrow Q^{\prime}(-8,24)$$R(3,7)\rightarrow R^{\prime}(3\times4,7\times4)\rightarrow R^{\prime}(12,28)$$S(6,4)\rightarrow S^{\prime}(6\times4,4\times4)\rightarrow S^{\prime}(24,16)$

We can see from the above coordinates of the vertices of the image that an enlargement occurred since the coordinates of the image are 4 times larger than that of the pre-image.