Question

△ABC is mapped to △A′B′C′ using each of the given rules.

Answer 1

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.

Answer 2

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)

Explanation:

1.The transformation (x, y)→(x+3, y-4) is a translation ,where the x coordinates of points of ΔABC translate 3 units toward right and the y coordinate translate 4 units downwards .Translation is rigid transformation which does not change the size of the figure, it just translate every point of a figure by a fixed distance to create its image. Thus this would result in △ABC being congruent to △A′B′C′.

2.The transformation (x, y)→(3x, 3y) is a dilation by a factor of 3.Since after dilation the size of image becomes different, thus this would result in △ABC being not congruent to △A′B′C′.

3.The transformation (x, y)→(0.4x, 0.4y) is a dilation by a factor of 0.4.Since after dilation the size of image becomes different, thus this would result in △ABC being not congruent to △A′B′C′.  

4.The transformation (x, y)→(x/3, y/3) is a dilation by a factor of 1/3. Since after dilation the size of image becomes different, thus this would result in △ABC being not congruent to △A′B′C′.

5.The transformation (x, y)→(-x, -y) is a reflection. Reflection is a rigid transformation which does not change the size of the figure, it create exactly same sized image of the original figure, Thus this would result in △ABC being congruent to △A′B′C′.