Question

graph the image of \\( \delta u v w \\) after a reflection over the line \\( y = - x \\).

Explanation:

Step1: Find the coordinates of \(U\), \(V\), \(W\)

Assume \(U(-7,-4)\), \(V(1,-4)\), \(W(-5,-9)\)

Step2: Apply the reflection rule over \(y = -x\)

The rule for reflection over the line \(y=-x\) is \((x,y)\to(-y,-x)\)
For point \(U(-7,-4)\):
Substitute \(x=-7\), \(y = -4\) into the rule \((x,y)\to(-y,-x)\)
\(U'=(4,7)\)
For point \(V(1,-4)\):
Substitute \(x = 1\), \(y=-4\) into the rule \((x,y)\to(-y,-x)\)
\(V'=(4,-1)\)
For point \(W(-5,-9)\):
Substitute \(x=-5\), \(y=-9\) into the rule \((x,y)\to(-y,-x)\)
\(W'=(9,5)\)

Step3: Plot the new points \(U'(4,7)\), \(V'(4,-1)\), \(W'(9,5)\) and connect them to form \(\triangle U'V'W'\)

Answer:

Plot the points \(U'(4,7)\), \(V'(4,-1)\), \(W'(9,5)\) and connect them.