Question

reflections on the coordinate plane
#3. the table represents the location of qrst before and after a reflection.
pre - image image
q(-9, -8) q’(9, -8)
r(-9, -2) r(9, -2)
s(-4, -2) s(4, -2)
t(-4, -8)?
give a verbal description of the transformation.

Explanation:

Step1: Identify coordinate transformation rule

For each pre-image point $(x,y)$, the image point is $( -x,y)$.
Example: $Q(-9,-8) \to Q'(9,-8)$ where $-(-9)=9$, $y=-8$ stays same.

Step2: Apply rule to point T

Pre-image $T(-4,-8)$: $x=-4$, so $-x = -(-4)=4$, $y=-8$ remains.
Expression: $T' = (4, -8)$

Step3: Describe the transformation

This rule matches reflection over the y-axis (the line $x=0$), which flips the sign of the x-coordinate while keeping the y-coordinate unchanged.

Answer:

The coordinates of $T'$ are $(4, -8)$.
The transformation is a reflection over the y-axis (the vertical line $x=0$), where each point's x-coordinate is negated and the y-coordinate stays the same.