Question

4b. is figure efgh the image of figure abcd after a reflection using line l? explain your reasoning with math vocabulary.

Explanation:

Step1: Recall reflection properties

In a reflection, corresponding points are equidistant from the line of reflection.

Step2: Check point - to - line distances

Measure the perpendicular distances from points A, B, C, D to line L and compare with distances from E, F, G, H to line L. Also, check if line L is the perpendicular bisector of the segments joining corresponding points (e.g., AA', BB', CC', DD' where A' is the corresponding point of A in the supposed reflection, etc.). If we assume the orientation and position of the figures, we can see that the orientation of Figure EFGH is not consistent with what would be expected from a reflection of Figure ABCD across line L. In a reflection, the pre - image and image are mirror images of each other with respect to the line of reflection. Here, the relative positions of the vertices do not match the reflection criteria.

Answer:

No, Figure EFGH is not the image of Figure ABCD after a reflection using line L because the orientation and relative positions of the vertices of the two figures do not satisfy the properties of a reflection (corresponding points are not equidistant from line L and line L is not the perpendicular bisector of the segments joining corresponding points).