Question

2 reflect triangle def over the x - axis. then answer a - c. a. record the vertices of the pre - image and the image in the table. pre - image image d e f b. describe how the reflection affected the x and y - values of each vertex. x - values: the same y - values: sign is reversed c. how could you represent a reflection over the x - axis algebraically?

Explanation:

Step1: Identify pre-image vertices

From the graph:
$D(-2, 2)$, $E(-7, 7)$, $F(-7, 2)$

Step2: Apply x-axis reflection rule

For a point $(x,y)$, reflection over x-axis is $(x, -y)$.

• $D'(-2, -2)$
• $E'(-7, -7)$
• $F'(-7, -2)$

Step3: Complete part a table

Organize pre-image and image points.

Step4: Analyze coordinate changes (part b)

Compare x/y values of pre-image and image.

Step5: Write algebraic rule (part c)

Generalize the reflection transformation.

Answer:

a. Table of Vertices:

PRE-IMAGE	IMAGE
$E(-7, 7)$	$E'(-7, -7)$
$F(-7, 2)$	$F'(-7, -2)$

b. Coordinate Changes:

• x-values: Remain unchanged
• y-values: Sign is reversed (positive becomes negative, negative becomes positive)

c. Algebraic Representation:

For any point $(x, y)$ in the pre-image, its image after reflection over the x-axis is given by:

$$(x, y) ightarrow (x, -y)$$