Question

Trapezoid JKLM with vertices (3, 4), K(6, 4), L(8, 1), and M(1, 1): 270° counterclockwise.

a. Quadrilateral is flipped vertically.
b. Quadrilateral is flipped horizontally.
c. Quadrilateral is rotated 90° clockwise.
d. Quadrilateral is rotated 180° clockwise.

Answer 1

The geometric transformation applied to Trapezoid JKLM is a vertical flip. So, option A. The quadrilateral is flipped vertically is correct.

Step-by-step explanation:

The given trapezoid JKLM has vertices at (3, 4), K(6, 4), L(8, 1), and M(1, 1). To flip the quadrilateral vertically, we need to change the sign of the y-coordinates while keeping the x-coordinates unchanged. So, the new vertices will be J'(3, -4), K'(6, -4), L'(8, -1), and M'(1, -1).

In mathematical terms, if (x, y) are the coordinates of a point in the original trapezoid, the corresponding coordinates in the vertically flipped trapezoid (J'K'L'M') would be (x, -y). Therefore, the answer to the question is that the quadrilateral is flipped vertically.

This transformation involves a reflection across the x-axis, resulting in a change in the orientation of the trapezoid with respect to the original. Each corresponding point on the reflected trapezoid has the same x-coordinate but an inverted y-coordinate. This process creates a mirror image of the original trapezoid with respect to the x-axis, demonstrating a vertical flip.
So, option A. The quadrilateral is flipped vertically is correct.