Question

select the correct answer.
polygon abcd is reflected and dilated to give polygon pqrs. the coordinates of the preimage are (2, 2), (6, 8), (12, 8), and (16, 2). the coordinates of the image are (11, 15), (9, 12), (6, 12), and (4, 15). what is the scale factor of the dilation?
a. 0.25
b. 0.33
c. 0.5
d. 0.75

Explanation:

Step1: Calculate the distance between two points in pre - image

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For points \(A(2,2)\) and \(B(6,8)\) in pre - image:

$$
LATEXBLOCK0
$$

Step2: Calculate the distance between two corresponding points in image

For points \(R(9,12)\) and \(S(11,15)\) in image:

$$
LATEXBLOCK1
$$

Step3: Find the scale factor

The scale factor \(k=\frac{d_{RS}}{d_{AB}}\). Substitute \(d_{AB}=2\sqrt{13}\) and \(d_{RS}=\sqrt{13}\) into the formula:

$$k=\frac{\sqrt{13}}{2\sqrt{13}} = 0.5$$

Answer:

C. \(0.5\)