Question

reflections
apply your knowledge of reflections to answer each question below.
a use the graph of triangle jkl to answer 1-2.

1. reflect jkl over the x-axis. record the coordinates of

the image below.
j ____ k __ l ____

1. write an algebraic representation for the reflection.

______
b the table represents the location of qrst before and after a reflection. use the table to
answer 3-5.
pre-image image
q(-9, -8) q(9, -8)
r(-9, -2) r(9, -2)
s(-4, -2) s(4, -2)
t(-4, -8) 4 ? -8

1. give a verbal description of the transformation.
2. which best represents the transformation algebraically?

a. (x, -y) b. (-x, y) c. (-x, -y) d. (x + 18, y)

1. find the location of t. 4 ? -8

c use the graph to mark each statement as true or false. correct any false statements.
f 6. the pre-image is in quadrant ii.
______ 7. the orientation of the vertices changed.
______ 8. the reflection can be represented by (-x, y).
______ 9. the line of reflection is the x-axis.
______ 10. the pre-image and image are congruent.

Explanation:

Step1: Identify coordinates of J, K, L

From the graph, find coordinates:

• \( J(-7, -7) \)
• \( K(-5, -2) \)
• \( L(-2, -3) \)

Step2: Reflect over x - axis

Rule for reflection over x - axis: \((x, y) \to (x, -y)\)

• For \( J(-7, -7) \): \( J'(-7, 7) \)
• For \( K(-5, -2) \): \( K'(-5, 2) \)
• For \( L(-2, -3) \): \( L'(-2, 3) \)

Step3: Algebraic representation

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

Answer:

1. \( J'(-7, 7) \), \( K'(-5, 2) \), \( L'(-2, 3) \)
2. \((x, y) \to (x, -y)\)