Question

graph the image of rectangle stuv after a reflection over the line ( y = x ).

Explanation:

Step1: Find the coordinates of the original rectangle

Assume the coordinates of rectangle \(STUV\) are \(S(2,8)\), \(T(4,8)\), \(U(4,9)\), \(V(2,9)\) (based on the graph).

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 \(S(2,8)\): \((2,8)\to(8,2)\)
• For point \(T(4,8)\): \((4,8)\to(8,4)\)
• For point \(U(4,9)\): \((4,9)\to(9,4)\)
• For point \(V(2,9)\): \((2,9)\to(9,2)\)

Step3: Plot the new points

Plot the points \((8,2)\), \((8,4)\), \((9,4)\), \((9,2)\) on the coordinate - plane and connect them to form the reflected rectangle.

Answer:

The coordinates of the reflected rectangle are \(S'(8,2)\), \(T'(8,4)\), \(U'(9,4)\), \(V'(9,2)\). Plot these points and connect them to get the image of rectangle \(STUV\) after reflection over \(y = x\).