Question

select the correct answer from each drop - down menu. triangle abc is dilated by a scale factor of 4 to form triangle abc.

Explanation:

Step1: Identify Coordinates of ABC

First, find the coordinates of triangle \( ABC \). From the graph:

• \( A(1, 2) \)
• \( B(3, 3) \)
• \( C(3, 1) \)

Step2: Apply Dilation (Scale Factor 4)

Dilation about the origin (assuming center is origin, as no other center is given) multiplies each coordinate by the scale factor (\( k = 4 \)):

• For \( A(1, 2) \): \( A'(1 \times 4, 2 \times 4) = (4, 8) \)
• For \( B(3, 3) \): \( B'(3 \times 4, 3 \times 4) = (12, 12) \)
• For \( C(3, 1) \): \( C'(3 \times 4, 1 \times 4) = (12, 4) \)

(Note: If the center of dilation was different, the process would adjust, but typically, if not specified, origin is assumed. The key is multiplying each coordinate by the scale factor.)

Answer:

The coordinates of \( A'B'C' \) after dilation by scale factor 4 (assuming center at origin) are \( A'(4, 8) \), \( B'(12, 12) \), \( C'(12, 4) \). (If the question was about a specific property like side length, area, etc., adjust accordingly. For example, side length of \( AB \) in \( ABC \): distance \( \sqrt{(3 - 1)^2 + (3 - 2)^2} = \sqrt{4 + 1} = \sqrt{5} \), so in \( A'B'C' \), it would be \( 4\sqrt{5} \).)