Question

graph the image of \\( \triangle tuv \\) after a reflection over the line \\( y = x \\).

Explanation:

Step1: Recall the reflection rule

When reflecting a point \((x,y)\) over the line \(y = x\), the transformation rule is \((x,y)\to(y,x)\).

Step2: Identify the coordinates of \(\triangle TUV\)

Assume \(T(x_1,y_1)\), \(U(x_2,y_2)\), \(V(x_3,y_3)\). Suppose \(T(-1, - 6)\), \(U(1,-6)\), \(V(-3,-7)\) (assuming coordinates based on grid - like structure).

Step3: Apply the reflection rule

For point \(T(-1,-6)\), after reflection over \(y = x\), the new point \(T'(-6,-1)\).
For point \(U(1,-6)\), after reflection over \(y = x\), the new point \(U'(-6,1)\).
For point \(V(-3,-7)\), after reflection over \(y = x\), the new point \(V'(-7,-3)\).

Step4: Plot the new points

Plot \(T'(-6,-1)\), \(U'(-6,1)\), \(V'(-7,-3)\) on the coordinate plane and connect them to form the image of \(\triangle TUV\) after reflection over the line \(y = x\).

Answer:

Plot the points obtained by applying the \((x,y)\to(y,x)\) transformation to each vertex of \(\triangle TUV\) and connect them.