Question

1. rotation 180° about the origin. reflection across the x-axis.

original
w(-5,3)
y(-3,1)
x(-3,4)
first
second

Explanation:

Step1: Rotate 180° about origin

The rule for a \( 180^\circ \) rotation about the origin is \( (x,y) \to (-x,-y) \).

• For \( W(-5,3) \): \( (-(-5), -3) = (5, -3) \)
• For \( Y(-3,1) \): \( (-(-3), -1) = (3, -1) \)
• For \( X(-3,4) \): \( (-(-3), -4) = (3, -4) \)

Step2: Reflect across x - axis

The rule for reflection across the \( x \) - axis is \( (x,y) \to (x,-y) \).

• For \( W(5, -3) \): \( (5, -(-3)) = (5, 3) \)
• For \( Y(3, -1) \): \( (3, -(-1)) = (3, 1) \)
• For \( X(3, -4) \): \( (3, -(-4)) = (3, 4) \)

Answer:

First transformation (180° rotation) points: \( W(5, -3) \), \( Y(3, -1) \), \( X(3, -4) \); Second transformation (x - axis reflection) points: \( W(5, 3) \), \( Y(3, 1) \), \( X(3, 4) \)