Question

write the notation to describe the movement of the points in the reflection below.
$g(1,3) \
ightarrow g(1,-3)$

a $r_{x-\text{axis}}$

b $r_{y-\text{axis}}$

c $r_{y=x}$

d $r_{y=-x}$

Explanation:

To determine the reflection notation, we analyze the transformation of point \( G(1, 3) \) to \( G'(1, -3) \).

• For a reflection over the \( x \)-axis (\( r_{x\text{-axis}} \)), the rule is \( (x, y) \to (x, -y) \). Applying this to \( G(1, 3) \), we get \( (1, -3) \), which matches \( G' \).
• For a reflection over the \( y \)-axis (\( r_{y\text{-axis}} \)), the rule is \( (x, y) \to (-x, y) \), which would give \( (-1, 3) \), not matching.
• For \( r_{y = x} \), the rule is \( (x, y) \to (y, x) \), giving \( (3, 1) \), not matching.
• For \( r_{y=-x} \), the rule is \( (x, y) \to (-y, -x) \), giving \( (-3, -1) \), not matching.

So the correct reflection is over the \( x \)-axis.

Answer:

a. \( r_{x\text{-axis}} \)