Plot triangle ABC on graph paper with points A(2,2). B(-2, -2) and C(8, -2).

a. Use the function (x, y) ==> (-1x, -1y) to transform triangle ABC. Graph and connect the new points then label this triangle A' B' C'. Describe how triangle ABC has been transformed. What, if anything, about the original triangle has been preserved in its image?

b. Now use the function (x,y) ==>(-2x, -2y) to transform the original triangle ABC to create triangle A"B"C". Has triangle ABC has undergone a rigid transformation to create A"B"C"? What, if anything, about the original triangle has been preserved in its image?

a) The new triangle is a reflection of the original across the origin. All angles, segment lengths, and line slopes have been preserved: the transformed triangle is congruent with the original.

b) The new triangle is a reflection of the original across the origin and a dilation by a factor of 2. Angles have been preserved: the transformed triangle is similar to the original. The transformation is NOT rigid.

Step-by-step explanation:

1. The transformed triangle is blue in the attachment. It is congruent with the original. The transformation is "rigid," a reflection across the origin. All angles and lengths have been preserved, as well as line slopes.

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2. The transformed triangle is orange in the attachment. It is similar to the original, in that angles have been preserved and lengths are proportional. It is a reflection across the origin and a dilation by a factor of 2. Line slopes have also been preserved. A dilation is NOT a "rigid" transformation.