Question

reflections on a coordinate plane
a. reflect the shape across the y - axis.
b. record the coordinates of each vertex before and after the reflection in the table.
preimage
a (, )
b (, )
c (, )
d (, )
image
a (, )
b (, )
c (, )
d (, )
c. use your table to write a rule that shows how the coordinates change when a shape is reflected across the y - axis.

Explanation:

Step1: Identify preimage coordinates

From the graph:
$A(4,1)$, $B(6,1)$, $C(6,4)$, $D(4,5)$

Step2: Apply y-axis reflection rule

Reflection across y-axis: $(x,y)\to(-x,y)$
Calculate image coordinates:
$A'(-4,1)$, $B'(-6,1)$, $C'(-6,4)$, $D'(-4,5)$

Step3: Summarize reflection rule

Generalize coordinate change for y-axis reflection.

Answer:

Completed Table:

Preimage	Image
$B(6,1)$	$B'(-6,1)$
$C(6,4)$	$C'(-6,4)$
$D(4,5)$	$D'(-4,5)$

Reflection Rule:

When a point $(x,y)$ is reflected across the y-axis, its new coordinates are $(-x,y)$ (the x-coordinate is negated, while the y-coordinate stays the same).