Question

the table represents the location of qrst before and after a reflection. use the table to answer 3-5.

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.

pre-image	image
r(-9, -2)	r(9, -2)
s(-4, -2)	s(4, -2)
t(-4, -8)	?

Explanation:

Step1: Analyze reflection pattern

Compare pre-image and image coordinates:
For $Q(-9, -8) \to Q'(9, -8)$, $R(-9, -2) \to R'(9, -2)$, $S(-4, -2) \to S'(4, -2)$: the $x$-coordinate is negated, $y$-coordinate stays the same.

Step2: Answer question 3

This transformation is a reflection over the $y$-axis (since only $x$-values flip sign, $y$ remains unchanged).

Step3: Answer question 4

The algebraic rule for negating $x$ while keeping $y$ is $(-x, y)$.

Step4: Find T' using the rule

Apply $(-x, y)$ to $T(-4, -8)$:
$x=-4$, so $-x = -(-4)=4$; $y=-8$ stays the same.
Expression: $T' = (4, -8)$

Answer:

1. Reflection over the y-axis
2. b. $(-x, y)$
3. $(4, -8)$