Question

graph the image of rectangle klmn after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Find coordinates of original points

The coordinates of rectangle \(KLMN\) are \(K(4,2)\), \(L(5,2)\), \(M(5,10)\), \(N(4,10)\).

Step2: Apply rotation rule

The rule for a \(90^{\circ}\) counter - clockwise rotation around the origin is \((x,y)\to(-y,x)\).
For point \(K(4,2)\): \((4,2)\to(- 2,4)\).
For point \(L(5,2)\): \((5,2)\to(-2,5)\).
For point \(M(5,10)\): \((5,10)\to(-10,5)\).
For point \(N(4,10)\): \((4,10)\to(-10,4)\).

Step3: Plot new points

Plot the new points \((-2,4)\), \((-2,5)\), \((-10,5)\), \((-10,4)\) and connect them to form the rotated rectangle.

Answer:

The new coordinates of the rectangle after a \(90^{\circ}\) counter - clockwise rotation around the origin are \(K'(-2,4)\), \(L'(-2,5)\), \(M'(-10,5)\), \(N'(-10,4)\). Plot these points on the coordinate plane.