Question

△bcd is dilated by a scale factor of \\(\frac{1}{3}\\) with the center of dilation at the origin. what are the coordinates of point c? (\\(\square\\), ?)

Explanation:

Step1: Find coordinates of C

From the graph, point \( C \) has coordinates \( (6, 6) \).

Step2: Apply dilation formula

Dilation with scale factor \( k = \frac{1}{3} \) centered at the origin: \( (x', y') = (k \cdot x, k \cdot y) \).
For \( C(6, 6) \), \( x' = \frac{1}{3} \cdot 6 = 2 \), \( y' = \frac{1}{3} \cdot 6 = 2 \).

Answer:

\((2, 2)\)