Question

1. reflect across the x-axis

grid with points w, x, y, z
w( , ) → w( , )
x( , ) → x( , )
y( , ) → y( , )
z( , ) → z( , )

Explanation:

Step1: Find coordinates of original points

• For point \( W \): From the graph, it's on the x - axis at \( (-2, 0) \).
• For point \( X \): From the graph, its coordinates are \( (1, - 2) \).
• For point \( Y \): From the graph, its coordinates are \( (-2, - 4) \).
• For point \( Z \): From the graph, its coordinates are \( (-5, - 2) \).

Step2: Apply reflection over x - axis rule

The rule for reflecting a point \( (x,y) \) over the x - axis is \( (x,y)\to(x, - y) \).

• For \( W(-2,0) \): Using the rule, \( W'=(-2,-0)=(-2,0) \) (since \( - 0 = 0 \)).
• For \( X(1, - 2) \): Using the rule, \( X'=(1,-(-2))=(1,2) \).
• For \( Y(-2, - 4) \): Using the rule, \( Y'=(-2,-(-4))=(-2,4) \).
• For \( Z(-5, - 2) \): Using the rule, \( Z'=(-5,-(-2))=(-5,2) \).

Answer:

\( W(-2,0)\to W'(-2,0) \)
\( X(1, - 2)\to X'(1,2) \)
\( Y(-2, - 4)\to Y'(-2,4) \)
\( Z(-5, - 2)\to Z'(-5,2) \)