Question

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.

pre - image	image

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.

pre - image	image

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: Fill reflection definition blanks

1. A reflection flips a figure over a line of reflection in order to create a congruent image.
2. Each reflected point of the figure should be the same distance from the line of reflection on the opposite side.

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For Problem 1 (Reflect over y-axis):

Step2: Identify pre-image vertices

From the graph:

• $W=(2,6)$, $X=(7,3)$, $Y=(2,1)$

Step3: Calculate image vertices

Reflection over y-axis: $(x,y)\to(-x,y)$

• $W'=(-2,6)$, $X'=(-7,3)$, $Y'=(-2,1)$

Step4: Analyze coordinate changes

• x-values: Sign is reversed
• y-values: Remain unchanged

Step5: Write algebraic rule

Reflection over y-axis: $(x,y)\to(-x,y)$

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For Problem 2 (Reflect over x-axis):

Step6: Identify pre-image vertices

From the graph:

• $D=(2,-2)$, $E=(7,-7)$, $F=(2,-7)$

Step7: Calculate image vertices

Reflection over x-axis: $(x,y)\to(x,-y)$

• $D'=(2,2)$, $E'=(7,7)$, $F'=(2,7)$

Step8: Analyze coordinate changes

• x-values: Remain unchanged
• y-values: Sign is reversed

Step9: Write algebraic rule

Reflection over x-axis: $(x,y)\to(x,-y)$

Answer:

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Reflection Definition Blanks:

1. flips, reflection, congruent
2. reflection

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Problem 1:

a.

PRE-IMAGE	IMAGE
$X(7,3)$	$X'(-7,3)$
$Y(2,1)$	$Y'(-2,1)$

b.

• x-values: Sign is reversed
• y-values: Stay the same

c. $(x,y)\to(-x,y)$

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Problem 2:

a.

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

b.

• x-values: Stay the same
• y-values: Sign is reversed

c. $(x,y)\to(x,-y)$