Which is the only geometric transformation where the image is NOT congruent to the pre-image?
The only geometric transformation where the image is NOT congruent to the pre-image is a Shear transformation.
The only geometric transformation where the image is NOT congruent to the pre-image is a shear transformation.
The only geometric transformation where the image is NOT congruent to the pre-image is a non-uniform scaling.
To understand why, let's first define congruence in geometry. Two figures are congruent if they have the same shape and size. When a geometric transformation is applied to a figure, the pre-image refers to the original figure, and the image refers to the transformed figure.
Now, let's consider the different types of geometric transformations:
1. Translation: This transformation slides a figure in a certain direction without changing its shape or size. The pre-image and the image remain congruent.
2. Rotation: This transformation rotates a figure about a fixed point without changing its shape or size. The pre-image and the image remain congruent.
3. Reflection: This transformation flips a figure across a line, known as the line of reflection, without changing its shape or size. The pre-image and the image remain congruent.
4. Dilation: This transformation scales a figure by a constant factor, enlarging or shrinking it uniformly in all directions. The pre-image and the image are similar but not necessarily congruent, as their sizes differ.
5. Non-uniform scaling: This transformation scales a figure by different factors along different axes. It changes the shape of the figure while also changing its size. Therefore, the pre-image and the image are not congruent.
In summary, non-uniform scaling is the only geometric transformation where the image is NOT congruent to the pre-image because its shape is altered along with the change in size.