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 the rule for reflection across y = -x

The rule for reflecting a point (x, y) across the line y=-x is (x,y)→(-y,-x).

Step2: Test each option

Option 1: For point (-4,-4)

Applying the rule (x,y)→(-y,-x), when x = - 4 and y=-4, we get -y = 4 and -x = 4. The new - point is (4,4), not (-4,-4).

Option 2: For point (-4,0)

Applying the rule (x,y)→(-y,-x), when x=-4 and y = 0, we get -y = 0 and -x = 4. The new - point is (0,4), not (-4,0).

Option 3: For point (0,-4)

Applying the rule (x,y)→(-y,-x), when x = 0 and y=-4, we get -y = 4 and -x = 0. The new - point is (4,0), not (0,-4).

Option 4: For point (4,-4)

Applying the rule (x,y)→(-y,-x), when x = 4 and y=-4, we get -y = 4 and -x=-4. The new - point is (4,-4), which is the same as the original point.

Answer:

(4, -4)