Question

2 find the scale factor of trapezoid qrst if it is dilated to qrst. type your result in the empty box provided below.

Explanation:

Step1: Select a corresponding side

Let's consider the vertical side of the trapezoids. For example, the vertical - distance from \(Q\) to \(S\) and from \(Q'\) to \(S'\). Suppose the coordinates of \(Q=(x_1,y_1)\), \(S=(x_2,y_2)\), \(Q'=(x_3,y_3)\), \(S'=(x_4,y_4)\). Count the grid - units. Let's assume the vertical distance from \(Q\) to \(S\) is \(d_1\) grid - units and from \(Q'\) to \(S'\) is \(d_2\) grid - units.
If we count the grid - units, assume the vertical distance from \(Q\) to \(S\) is \(4\) units and the vertical distance from \(Q'\) to \(S'\) is \(8\) units.

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the ratio of the lengths of the corresponding sides of the dilated figure and the original figure. For two corresponding sides \(a\) (original) and \(b\) (dilated), \(k=\frac{b}{a}\). Here, \(k = \frac{\text{length of }Q'S'}{\text{length of }QS}\). Since \(\frac{8}{4}=2\), the scale factor of the dilation.

Answer:

2