Question

The figure shows three parallelograms: ABCD, A′B′C′D′, and A″B″C″D″.

Answer 1

Parallelogram ABCD is reflected across the x-axis to create parallelogram A'B'C'D'. Parallelogram A'B'C'D' maintains the same distance from the x-axis for all points. Parallelogram ABCD has positive x-values and positive y-values, and parallelogram A'B'C'D' has positive x-values and negative y-values, which also define this transition.

Parallelogram ABCD has positive x-values and positive y-values. Parallelogram A''B''C''D'' has negative x-values and positive y-values. If we look at point B in both parallelograms, point B in ABCD is located at point (2,3), and point B in A''B''C''D'' is located at point (-3, 2). This means that parallelogram A'B'C'D' was rotated about the origin 270 degrees clockwise, or 90 degrees counter-clockwise, due to the flipping of x and y values and the change in the x-value's sign.