△ABC is mapped to △A′B′C′ using each of the given rules.Which rules would result in △ABC being congruent to or not congruent to △A′B′C′ ?Drag and drop each rule into the boxes to classify it as Congruent or Not Congruent.

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 not 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.