Question

select the construction that guarantees ( a ) is a reflection of point ( a ) across line ( bc ).
select the correct choice.
a
construction a
b
construction b ( a d perp b d )
c
construction c ( a d perp b d )
d
construction d ( a d perp b d )

Explanation:

Step1: Recall the property of reflection

When a point \(A\) is reflected across a line \(BC\), the line \(BC\) is the perpendicular bisector of the segment joining \(A\) and its reflection \(A'\). That is, \(AA'\perp BC\) and \(AD = A'D\) (where \(D\) is the intersection point of \(AA'\) and \(BC\)).

Step2: Analyze each construction

• Construction A: The line \(BC\) is not the perpendicular bisector of \(AA'\).
• Construction B: Here \(AA'\perp BC\) (as indicated by the right - angle symbol) and \(AD = A'D\). This satisfies the condition for a reflection across the line \(BC\).
• Construction C: The relationship shown does not meet the requirements for a reflection across line \(BC\) (the perpendicularity and equal - distance conditions are not met as per the reflection property).
• Construction D: The given relationship \(AD = BD\) is not relevant to the reflection of \(A\) across line \(BC\).

Answer:

B. Construction B \(AA'\perp BC\) and \(AD = A'D\)