Question

this diagram shows how lin tried to reflect triangle abc across line l. she knows something went wrong because the image isnt congruent to the original figure. 1. what is one idea that lin probably understands about reflections? 2. what is one idea that lin doesnt understand about reflections?

Explanation:

1. Lin likely understands that points are mapped to new positions across the line of reflection. She has attempted to create new points \(A'\), \(B'\), \(C'\) for the reflected triangle, showing an understanding that the original points \(A\), \(B\), \(C\) have corresponding points on the other - side of the line \(l\).
2. Lin doesn't understand that the distance from a point to the line of reflection should be equal to the distance from its image to the line of reflection. In a proper reflection, the perpendicular distances from \(A\), \(B\), \(C\) to line \(l\) should be the same as the perpendicular distances from \(A'\), \(B'\), \(C'\) to line \(l\). Since the image is not congruent to the original, this key property of reflections has been violated.

Answer:

1. She understands that points are mapped across the line of reflection to get new corresponding points.
2. She doesn't understand that the distance from a point to the line of reflection is equal to the distance from its image to the line of reflection.