Question

select the correct graph. which image shows triangle abc dilated by a scale factor of 3 centered at the point b? images of triangles and a reset and next button are present

Explanation:

Step1: Recall Dilation Center

Dilation centered at \( B \) means \( B \) is the fixed point (image of \( B \) is \( B \) itself, \( B' = B \)).

Step2: Check Scale Factor 3

For a scale factor of 3, the distance from \( B \) to \( A' \) should be 3 times the distance from \( B \) to \( A \), and distance from \( B \) to \( C' \) should be 3 times the distance from \( B \) to \( C \).

Step3: Analyze Each Image

• Top - left: \( B'

eq B \), so center not \( B \). Eliminate.

• Top - right: Original triangle, no dilation. Eliminate.
• Bottom - left: \( B' = B \), check distances. \( BA' = 3BA \), \( BC' = 3BC \). Matches dilation by 3 centered at \( B \).
• Bottom - right: \( B' = B \), but \( BA' \) and \( BC' \) do not seem 3 times. Eliminate.

Answer:

The bottom - left graph (the one with \( B \) as \( B' \), triangle \( A'B'C' \) and original triangle \( ABC \) with \( B \) common)