Which segment is the image of \(AB\) when rotated \(90^\circ\) counterclockwise around point \(P\)?

5 segments on a grid, with Point P in the center. H I, horizontal, length 3, bottom left. F G, vertical, length 3, top left. On the right of F G, E D, slanting up and to the right. A B and B C, create right angle at B. A B, horizontal, length 3, top right. B C, vertical, length 3.

Here are 2 polygons:

Two congruent polygons on isometric grid labeled polygon P and polygon Q. Polygon P is above Polygon Q and shares common point A. Polygon P, beginning at bottom left and moving clockwise, the points are B, C, D, E, and A. Polygon Q, in corresponding order to Polygon P and moving counter-clockwise, the points are A, F, G, H, and J.

Select all sequences of translations, rotations, and reflections below that would take polygon \(P\) to polygon \(Q\).

1. Draw the image of figure \(ABC\) when translated by directed line segment \(u\). Label the image of \(A\) as \(A’\), the image of \(B\) as \(B’\), and the image of \(C\) as \(C’\).
2. Explain why the line containing \(AB\) is parallel to the line containing \(A’B’\).

A figure and directed line segment u. Figure made of two line segments A B and B C. A B slants upward and to the right, B C is horizontal. Segments meet at endpoint B, form angle A B C. Below and to the right of the figure, directed line segment u. Horizontal, no endpoint on left end, arrow at right end.

There is a sequence of rigid transformations that takes \(A\) to \(A’\), \(B\) to \(B’\), and \(C\) to \(C’\). The same sequence takes \(D\) to \(D’\). Draw and label \(D’\):