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:

1. bella believes the graph shows a translation down while scott believes it shows a reflection over the x - axis. who is correct? explain.
2. triangle abc has the coordinates shown in the table. miguel is going to reflect the triangle using the rule ((x, y) \to (-x, y)).

a. what is the line of reflection?
b. list the coordinates of the image in the table. in which quadrant will the image lie?
in 6 - 8, use the description to identify the line of reflection and write an algebraic representation for the reflection.

1. point (a(8, -1)) is reflected to (a(-8, -1)).
2. a figure is reflected from quadrant i to iv.
3. point (z(-5, 7)) is reflected to (z(-5, -7)).

summarize today’s lesson:

Explanation:

Problem 3

Step1: Identify reflection axis

Original triangle $P(-6,4)$, $Q(-2,7)$, $R(-2,2)$; image $P'(6,4)$, $Q'(2,7)$, $R'(2,2)$. The $y$-coordinates stay same, $x$-coordinates flip sign.

Step2: Write algebraic rule

For any point $(x,y)$, the transformation flips the $x$-value.

Step3: Analyze figure properties

Reflections preserve size; reverse vertex/orientation order.

A translation down would shift all points straight down, keeping their $x$-coordinates identical and subtracting the same value from all $y$-coordinates. A reflection over the $x$-axis flips the sign of the $y$-coordinate: $(x,y)\to(x,-y)$. For the original vertices $L(-5,7)$, $M(-2,7)$, $N(-2,2)$, $O(-5,2)$, the image vertices are $L'(-5,-7)$, $M'(-2,-7)$, $N'(-2,-2)$, $O'(-5,-2)$, which matches the reflection rule, not a translation.

Step1: Identify reflection line

Rule $(x,y)\to(-x,y)$ flips $x$-coordinate sign, which is the $y$-axis definition.

Step2: Calculate image coordinates

Apply $(-x,y)$ to each pre-image point:

• $A(-4,-6)\to(4,-6)$
• $B(-5,-8)\to(5,-8)$
• $C(-1,-3)\to(1,-3)$

Step3: Identify quadrant

Points with positive $x$, negative $y$ lie in Quadrant IV.

Answer:

a. Reflection over the $y$-axis (vertical axis)
b. $(x,y)\to(-x,y)$
c.

• Size of the figure: Stayed the same
• Orientation of the figure: Changed
• Orientation of the vertices: Changed

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Problem 4