Question

question 1
the preimage and image of trapezoid abcd is shown in the coordinate plane below.
what is the transformation that takes place to produce the image from the preimage?
reflection across the x - axis
reflection across the y - axis
rotation
translation

Explanation:

Step1: Recall transformation rules

In a reflection across the x - axis, the rule is $(x,y)\to(x, - y)$. In a reflection across the y - axis, the rule is $(x,y)\to(-x,y)$. In a rotation, the orientation of the shape changes. In a translation, the shape moves without changing orientation or being flipped.

Step2: Analyze the trapezoid

For each vertex of trapezoid ABCD and its corresponding vertex in A'B'C'D', we can see that the x - coordinates remain the same and the y - coordinates change their signs. For example, if a vertex of the pre - image has coordinates $(x,y)$, the corresponding vertex of the image has coordinates $(x, - y)$. This is the rule for reflection across the x - axis.

Answer:

Reflection across the x - axis