which point would map onto itself after a reflection across the line ( y = -x )?\n( (-4,-4) )\n( (-4,0) )\n(…
which point would map onto itself after a reflection across the line ( y = -x )?\n( (-4,-4) )\n( (-4,0) )\n( (0,-4) )\n( (4,-4) )
Answer
Explanation:
Step1: Recall the reflection formula
When reflecting a point ((x,y)) across the line (y = -x), the formula is ((x,y)\to(-y,-x)).
Step2: Apply the formula to each point
- For ((-4,-4)): Using the formula ((x = - 4,y=-4)), we get ((-(-4),-(-4))=(4,4)\neq(-4,-4)).
- For ((-4,0)): Using the formula ((x=-4,y = 0)), we get ((-0,-(-4))=(0,4)\neq(-4,0)).
- For ((0,-4)): Using the formula ((x = 0,y=-4)), we get ((-(-4),-0)=(4,0)\neq(0,-4)).
- For ((4,-4)): Using the formula ((x = 4,y=-4)), we get ((-(-4),-4)=(4,-4)).
Answer:
((4,-4))