Question

for this item, select the answer from the drop - down menu that correctly completes the sentence. consider the trapezoid graphed on the coordinate plane. a transformation of will carry the trapezoid onto itself. a reflection across the x - axis a reflection across the y - axis a rotation of 180° about the origin a translation 2 units up

Explanation:

Step1: Recall transformation rules

A reflection across the x - axis changes the sign of the y - coordinates. A reflection across the y - axis changes the sign of the x - coordinates. A 180 - degree rotation about the origin changes the signs of both x and y coordinates. A translation moves the figure without changing its orientation or shape.

Step2: Analyze the trapezoid's symmetry

The trapezoid is symmetric about the y - axis. When we reflect a point (x,y) across the y - axis, it becomes (-x,y). For a figure symmetric about the y - axis, this transformation will map the figure onto itself.

Answer:

a reflection across the y - axis