Question

which point would map onto itself after a reflection across the line y = -x?
○ (-4, -4)
○ (-4, 0)
○ (0, -4)
○ (4, -4)

Explanation:

Step1: Recall reflection rule over \( y = -x \)

The rule for reflecting a point \( (x, y) \) over the line \( y=-x \) is \( (x, y)\to(-y, -x) \). A point maps onto itself if \( (x, y)=(-y, -x) \), which implies \( x=-y \) and \( y = -x \) (both simplify to \( x + y=0 \)).

Step2: Check each option

• For \( (-4, -4) \): \( x=-4, y = -4 \). Check \( x + y=-4+(-4)=-8

eq0 \).

• For \( (-4, 0) \): \( x=-4, y = 0 \). \( x + y=-4 + 0=-4

eq0 \).

• For \( (0, -4) \): \( x = 0, y=-4 \). \( x + y=0+(-4)=-4

eq0 \).

• For \( (4, -4) \): \( x = 4, y=-4 \). \( x + y=4+(-4)=0 \), so it satisfies \( x=-y \) (since \( 4=-(-4) \)) and \( y=-x \) (since \( -4=-4 \)).

Answer:

(4, -4)