Question

triangle abc has been reflected over the y-axis to create triangle abc. which of the following statements is true?
bc = 2
ab = 2
ab = 2
ac = 2

Explanation:

Step1: Recall reflection properties

Reflection over the y - axis is a rigid transformation. Rigid transformations (like reflection) preserve the lengths of sides of a figure. So, the corresponding sides of triangle \(ABC\) and its reflection \(A'B'C'\) are equal in length.

Step2: Analyze the given options

• For the option \(B'C' = 2\): Since \(B'C'\) is the reflection of \(BC\), if \(BC = 2\) (from the diagram, the side \(BC\) of triangle \(ABC\) is labeled with length 2), then by the property of reflection (rigid transformation), \(B'C'=BC = 2\).
• For \(A'B'=2\): \(A'B'\) is the reflection of \(AB\). There is no indication that \(AB = 2\) from the diagram (the side with length 2 is \(BC\)).
• For \(AB = 2\): The side labeled with length 2 is \(BC\), not \(AB\).
• For \(AC = 2\): The side labeled with length 2 is \(BC\), not \(AC\).

Answer:

\(B'C' = 2\) (the option corresponding to \(B'C' = 2\))