Question

A rectangle is graphed on a coordinate grid. Which transformation will result in a rectangle that is NOT congruent to the original rectangle?

Answer 1

A transformation that will result in a rectangle that is NOT congruent to the original rectangle is a non-uniform scaling transformation, also known as an anisotropic transformation. This occurs when you stretch or compress the rectangle in one direction (either vertically or horizontally) while leaving the other dimension unchanged.

For example, if you take a rectangle and stretch it vertically (e.g., multiply the y-coordinates by a factor greater than 1), the resulting shape will be a rectangle, but it will no longer be congruent to the original rectangle since the lengths of the sides will have changed. Other transformations that would not result in a congruent rectangle include shear transformations and any transformation that involves changing the angles or the ratio of side lengths.