Question

Which sequence of transformation will not result in a figure that is congruent to the original figure?

A) a rotation of 270° counter clockwise about the origin followed by translation of eight units to the right
B) A reflection over the Y axis followed by a rotation of 180° about the origin
C) a dilation with a scale factor of four followed by reflection over the x-axis
D) A reflection over the Y axis followed by a translation of 3 units to the left and 2 units to the right

Answer 1

The correct option is C.

Explanation:

Two figures are congruent if their corresponding sides are congruent.

We know that, reflection, rotation and translation are rigid transformation. It means the size and shape of image and preimage are same. We can say that in rigid transformation, the image and preimage are congruent.

Dilation is not a rigid transformation. It represents enlargement and compression.

If scale factor |k|>1, then it represent enlargement. If scale factor |k|<1, then it represent compression.

In option C, the scale factor is 4. It means the sides of image are 4 times of the preimage.

Therefore option C is correct and the resultant figure of option C is not congruent to the original figure.