Question

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

Explanation:

Step1: Find original coordinates

From the graph, the coordinates of \(Q(-6,0)\), \(P(-6, - 4)\), \(R(-8,-6)\)

Step2: Apply reflection formula

The rule for reflection over the line \(y=-x\) is \((x,y)\to(-y,-x)\)

For point \(Q(-6,0)\):
Substitute \(x = - 6\) and \(y = 0\) into \((x,y)\to(-y,-x)\)
\((-6,0)\to(0,6)\)

For point \(P(-6,-4)\):
Substitute \(x=-6\) and \(y = - 4\) into \((x,y)\to(-y,-x)\)
\((-6,-4)\to(4,6)\)

For point \(R(-8,-6)\):
Substitute \(x=-8\) and \(y=-6\) into \((x,y)\to(-y,-x)\)
\((-8,-6)\to(6,8)\)

Answer:

The coordinates of \(Q'\) is \((0,6)\), the coordinates of \(P'\) is \((4,6)\) and the coordinates of \(R'\) is \((6,8)\)