Question

select the conditions that guarantee b is a reflection of point a across line l.

Explanation:

Step1: Recall reflection property

In a reflection of a point \(A\) across a line \(l\), the line \(l\) is the perpendicular - bisector of the line segment joining \(A\) and its image \(B\). So, the distance from \(A\) to the line \(l\) is equal to the distance from \(B\) to the line \(l\), and the line segment \(AB\) is perpendicular to the line \(l\).

Step2: Analyze options

In the correct reflection, the lengths from the point \(A\) and its image \(B\) to the line of reflection \(l\) should be equal and the line segment \(AB\) should be perpendicular to \(l\). The option where the line segment joining \(A\) and \(B\) is perpendicular to \(l\) and the distances from \(A\) and \(B\) to \(l\) are equal is the correct one. In the case where the lengths from \(A\) and \(B\) to \(l\) are both \(7\) and \(AB\perp l\), it satisfies the properties of reflection.

Answer:

The option where the line segment \(AB\) is perpendicular to line \(l\) and the distance from \(A\) to \(l\) is equal to the distance from \(B\) to \(l\) (the one with lengths \(7\) from \(A\) and \(B\) to \(l\) and \(AB\perp l\))