Question

write the coordinates of the vertices after a reflection over the line $y = -x$.

Explanation:

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

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

Step2: Find the original coordinates

From the graph: \(P(-9,-9)\), \(Q(1,-9)\), \(R(-1,-2)\), \(S(-4,-2)\)

Step3: Apply the reflection rule

• For \(P(-9,-9)\):

\(x=-9,y = -9\), after reflection \((-y,-x)=(9,9)\)

• For \(Q(1,-9)\):

\(x = 1,y=-9\), after reflection \((-y,-x)=(9,-1)\)

• For \(R(-1,-2)\):

\(x=-1,y=-2\), after reflection \((-y,-x)=(2,1)\)

• For \(S(-4,-2)\):

\(x=-4,y=-2\), after reflection \((-y,-x)=(2,4)\)

Answer:

\(P(9,9)\)
\(Q(9,-1)\)
\(R(2,1)\)
\(S(2,4)\)