Question

1. a rectangle is plotted on the coordinate plane below. rotate the figure 90 degrees clockwise about the origin.

Explanation:

Step1: Find the original coordinates

The original vertices of the rectangle are \((0,0)\), \((6,0)\), \((6,2)\), \((0,2)\).

Step2: Apply the rotation formula

The formula for a \(90^{\circ}\) clockwise rotation about the origin is \((x,y)\to(y, -x)\).

• For \((0,0)\): \((0,0)\to(0,0)\)
• For \((6,0)\): \((6,0)\to(0,-6)\)
• For \((6,2)\): \((6,2)\to(2,-6)\)
• For \((0,2)\): \((0,2)\to(2,0)\)

Answer:

The new vertices of the rotated rectangle are \((0,0)\), \((0, - 6)\), \((2,-6)\), \((2,0)\). Plot these points on the coordinate plane to get the rotated rectangle.