Question

(2) sketch each preimage and its dilation. list the coo
a. quadrilateral abcd with vertices a(-4, 1),
b(-2, 3), c(0, -2), and d(-5, -2). 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 \( (x,y) \to (kx, ky) \).

Step2: Dilate Point A

Given \( A(-4, 1) \) and \( k = 3 \), apply the rule: \( A' = (3\times(-4), 3\times1) = (-12, 3) \).

Step3: Dilate Point B

Given \( B(-2, 3) \) and \( k = 3 \), apply the rule: \( B' = (3\times(-2), 3\times3) = (-6, 9) \).

Step4: Dilate Point C

Given \( C(0, -2) \) and \( k = 3 \), apply the rule: \( C' = (3\times0, 3\times(-2)) = (0, -6) \).

Step5: Dilate Point D

Given \( D(-5, -2) \) and \( k = 3 \), apply the rule: \( D' = (3\times(-5), 3\times(-2)) = (-15, -6) \).

Answer:

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