Question

reflections on the coordinate plane
reflections

• a reflection __ a figure over a line of in order to create a __ image.
• each reflected point of the figure should be the same distance from the line of ____ on the opposite side.

1 reflect triangle wxy over the y - axis. then answer a - c.
a. record the vertices of the pre - image and the image in the table.
b. describe how the reflection affected the x and y - values of each vertex.

• x - values:
• y - values:

c. how could you represent a reflection over the y - axis algebraically?
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.
b. describe how the reflection affected the x and y - values of each vertex.

• x - values:
• y - values:

c. how could you represent a reflection over the x - axis algebraically?

Explanation:

Step1: Identify pre-image vertices

From the graph, pre-image vertices: $D(2,-2)$, $F(2,-7)$, $E(6,-7)$

Step2: Reflect over x-axis rule

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

Step3: Calculate image vertices

• $D'(2, -(-2))=(2,2)$
• $F'(2, -(-7))=(2,7)$
• $E'(6, -(-7))=(6,7)$

Step4: Analyze coordinate changes

x-values stay unchanged; y-values sign flips.

Step5: Write algebraic representation

Use the reflection rule derived.

Answer:

2a.

PRE-IMAGE	IMAGE
$(2,-7)$	$(2,7)$
$(6,-7)$	$(6,7)$

2b.

• x-values: remain the same
• y-values: become the opposite sign

2c.

A reflection over the x-axis can be represented algebraically as $(x,y) \to (x,-y)$