△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.

- 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′.

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step-by-step explanation:

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