Question

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

Explanation:

Step1: Find the original coordinates

From the graph, we can see that the coordinates of \(U\) is \((-9,-7)\), \(V\) is \((-5,-7)\) and \(W\) is \((-4,2)\).

Step2: Apply the reflection rule

The rule for reflecting a point \((x,y)\) over the line \(y = -x\) is \((x,y)\to(-y,-x)\).
For point \(U(-9,-7)\):
Substitute \(x=-9\) and \(y = -7\) into the rule \((-y,-x)\), we get \((7,9)\).
For point \(V(-5,-7)\):
Substitute \(x=-5\) and \(y=-7\) into the rule \((-y,-x)\), we get \((7,5)\).
For point \(W(-4,2)\):
Substitute \(x = -4\) and \(y=2\) into the rule \((-y,-x)\), we get \((-2,4)\).

Answer:

The coordinates of \(U'\) is \((7,9)\), \(V'\) is \((7,5)\) and \(W'\) is \((-2,4)\).