Question

graph the image of trapezoid ( j k l m ) after a rotation ( 270^{circ} ) counterclockwise around the origin.

Explanation:

Step1: Determine the coordinates of the original trapezoid

The coordinates of the vertices of trapezoid \(JKLM\) are \(J(-8,1)\), \(K(-4,1)\), \(L(-6,10)\), \(M(-10,10)\)

Step2: Apply the rotation rule for \(270^{\circ}\) counter - clockwise

The rule for a \(270^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(y, - x)\)

• For point \(J(-8,1)\): \(x=-8,y = 1\), after rotation \(J'(1,8)\)
• For point \(K(-4,1)\): \(x=-4,y = 1\), after rotation \(K'(1,4)\)
• For point \(L(-6,10)\): \(x=-6,y = 10\), after rotation \(L'(10,6)\)
• For point \(M(-10,10)\): \(x=-10,y = 10\), after rotation \(M'(10,10)\)

Step3: Plot the new points

Plot the points \(J'(1,8)\), \(K'(1,4)\), \(L'(10,6)\), \(M'(10,10)\) on the coordinate plane and connect them to form the rotated trapezoid.

Answer:

The coordinates of the vertices of the rotated trapezoid are \(J'(1,8)\), \(K'(1,4)\), \(L'(10,6)\), \(M'(10,10)\). Plot these points and connect them to get the image of trapezoid \(JKLM\) after a \(270^{\circ}\) counter - clockwise rotation about the origin.