Question

(2) sketch each preimage and its dilation. list the coor
a. quadrilateral abcd with vertices a(-4, 1),
b(-2, 3), c(0, -2), and d(-5, -1) k = 3

a (__, __)
b (__, __)
c (__, __)
d (__, __)

Explanation:

Step1: Recall Dilation Rule

For a dilation with scale factor \( k \) centered at the origin, the rule is \( (x, y) \to (kx, ky) \). Here, \( k = 3 \).

Step2: Dilate Point A(-4, 1)

Apply the rule: \( A' = (3 \times -4, 3 \times 1) = (-12, 3) \)

Step3: Dilate Point B(-2, 3)

Apply the rule: \( B' = (3 \times -2, 3 \times 3) = (-6, 9) \)

Step4: Dilate Point C(0, -2)

Apply the rule: \( C' = (3 \times 0, 3 \times -2) = (0, -6) \)

Step5: Dilate Point D(-5, -1)

Apply the rule: \( D' = (3 \times -5, 3 \times -1) = (-15, -3) \)

Answer:

\( A'(-12, 3) \), \( B'(-6, 9) \), \( C'(0, -6) \), \( D'(-15, -3) \)