Question

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: Find the length of a side 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 \(B(6,8)\):

$$
LATEXBLOCK0
$$

Step2: Find the length of the corresponding side in the image

For points \(P(11,15)\) and \(S(4,15)\):

$$
LATEXBLOCK1
$$

Another way (using horizontal/vertical sides for simplicity):
Length of \(AD\) (pre - image, \(A(2,2)\) and \(D(16,2)\)): \(AD=\vert16 - 2\vert=14\)
Length of \(PS\) (image, \(P(11,15)\) and \(S(4,15)\)): \(PS=\vert11 - 4\vert = 7\)

Step3: Calculate the scale factor

Scale factor \(k=\frac{\text{length of image side}}{\text{length of pre - image side}}\)
Since \(AD = 14\) (pre - image) and \(PS=7\) (image), \(k=\frac{7}{14}=0.5\)

Answer:

C. 0.5