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 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 \((-(-4),-(-4))=(4,4)
eq(-4,-4)\).

• For \((-4,0)\):

Using the formula \((x=-4,y = 0)\), we get \((-0,-(-4))=(0,4)
eq(-4,0)\).

• For \((0,-4)\):

Using the formula \((x = 0,y=-4)\), we get \((-(-4),-0)=(4,0)
eq(0,-4)\).

• For \((4,-4)\):

Using the formula \((x = 4,y=-4)\), we get \((-(-4),-4)=(4,-4)\).

Answer:

\((4,-4)\)