Answer:
Congruent: (x, y)→(x+3, y-4); (x, y)→(-x, -y)
Not Congruent: (x, y)→(3x, 3y); (x, y)→(0.4x, 0.4y); (x, y)→(x/3, y/3)
Step-by-step explanation:
Transformations that result in congruent figures are translations, rotations and reflections. Translations that result in figures that are <em>not</em> congruent are dilations.
The first transformation, (x, y)→(x+3, y-4) is a translation 3 units to the right and 4 units down. This will result in congruent figures, since it only slides the figure.
The second transformation, (x, y)→(3x, 3y) is a dilation by a factor of 3. A dilation is a stretch or a shrink; a dilation factor of 3 will stretch the figure. Since it is stretched, it is not the same size and therefore not congruent.
The third transformation, (x, y)→(0.4x, 0.4y) is a dilation by a factor of 0.4. This dilation will shrink the figure. Since it is shrunk, it is not the same size and therefore not congruent.
The fourth transformation, (x, y)→(x/3, y/3) is a dilation by a factor of 1/3. This dilation will shrink the figure. Since it is shrunk, it is not the same size and therefore not congruent.
The fifth transformation, (x, y)→(-x, -y) is a reflection. This does not change the size of the figure, just the placement and orientation of it. Since the size is not changed, the figure is congruent.
