Question

1. (03.03 lc) parallelogram efgh has been reflected across the x - axis and then rotated 180 degrees around the origin. which of the following transformations would return the parallelogram to its original position? (5 points) reflection across the line y = x reflection across the x - axis reflection across the x - axis and then reflection across the y - axis reflection across the y - axis

Explanation:

Step1: Define a vertex point

Let a vertex of the parallelogram be $(x,y)$.

Step2: Reflect across x-axis

Reflecting $(x,y)$ over x-axis gives $(x,-y)$.

Step3: Rotate 180° around origin

Rotating $(x,-y)$ 180° around origin: $(x,-y) \to (-x,y)$.

Step4: Find inverse transformation

We need a transformation that maps $(-x,y)$ back to $(x,y)$. Test each option:

• Reflection over $y=x$: $(-x,y) \to (y,-x)

eq (x,y)$

• Reflection over x-axis: $(-x,y) \to (-x,-y)

eq (x,y)$

• Reflection over x-axis then y-axis: $(-x,y) \to (-x,-y) \to (x,-y)

eq (x,y)$

• Reflection over y-axis: $(-x,y) \to (x,y)$, which is the original point.

Answer:

Reflection across the y-axis