Question

1. use the reflection shown to complete each statement below: a. give a verbal description of the transformation. b. give an algebraic representation of the transformation. c. list if each of the following changed or stayed the same: size of the figure: orientation of the figure: orientation of the vertices: 4. bella believes the graph shows a translation down while scott believes it shows a reflection over the y - axis.

Explanation:

Step1: Identify the transformation type

The figure $\triangle PQR$ is reflected over the x - axis to get $\triangle P'Q'R'$.

Step2: Provide verbal description

The transformation is a reflection over the x - axis.

Step3: Provide algebraic representation

For a point $(x,y)$ reflected over the x - axis, the transformation rule is $(x,y)\to(x, - y)$. So for the vertices of $\triangle PQR$ with $P(5,7)$, $Q(7,4)$, $R(3,2)$ and their images $P'(5, - 7)$, $Q'(7, - 4)$, $R'(3, - 2)$ the rule $(x,y)\to(x, - y)$ is applied.

Step4: Analyze size, orientation of figure

The size of the figure stayed the same because a reflection is a rigid transformation which preserves distance and angle measures. The orientation of the figure changed because the pre - image and the image are mirror images of each other. The orientation of the vertices (e.g., the order of vertices in a counter - clockwise or clockwise sense) is reversed. The orientation of the vertices is reversed. For example, in $\triangle PQR$ the vertices may be in a counter - clockwise order and in $\triangle P'Q'R'$ they are in a clockwise order.

Answer:

a. The transformation is a reflection over the x - axis.
b. The algebraic representation of the transformation is $(x,y)\to(x, - y)$.
c. Size: Stayed the same; Orientation of the figure: Changed; Orientation of the vertices: Changed.