Question

3 describe a sequence of rigid motions that would map △abc onto △abc

Explanation:

Step1: Analyze Coordinates (Assume)

Assume coordinates: Let’s say \( A(x_1,y_1) \), \( B(x_2,y_2) \), \( C(x_3,y_3) \) for \( \triangle ABC \) and \( A'(x_1',y_1') \), \( B'(x_2',y_2') \), \( C'(x_3',y_3') \) for \( \triangle A'B'C' \). From the grid, observe translation and rotation.

Step2: Translation

First, translate \( \triangle ABC \) so that a corresponding vertex (e.g., \( A \)) moves closer to \( A' \). Calculate the horizontal and vertical shifts. Suppose \( A \) needs to move right by \( h \) units and down by \( v \) units.

Step3: Rotation

After translation, rotate the triangle about a point (e.g., the translated \( A \)) to align the sides with \( \triangle A'B'C' \). Determine the angle of rotation (e.g., \( 90^\circ \), \( 180^\circ \), or other) by comparing the slopes of corresponding sides.

Step4: Final Adjustment (if needed)

Check if further translation or rotation is needed to perfectly map \( \triangle ABC \) to \( \triangle A'B'C' \).

(Note: Since the image is partially visible, a general approach is provided. For a precise answer, the exact coordinates of the triangles are required.)

Answer:

A possible sequence: 1. Translate \( \triangle ABC \) horizontally and vertically to align a vertex with the corresponding vertex of \( \triangle A'B'C' \). 2. Rotate the translated triangle about that vertex to match the orientation of \( \triangle A'B'C' \). 3. Translate (if needed) to fully overlap \( \triangle ABC \) with \( \triangle A'B'C' \). (Exact steps depend on the coordinates of the triangles in the grid.)