Question

graph the image of square j k l m after a rotation 270° counterclockwise around the origin.

Explanation:

Step1: Determine the original coordinates

The coordinates of the square \(JKLM\) are \(J(-8,1)\), \(K(-2,1)\), \(L(-2,5)\), \(M(-8,5)\).

Step2: Apply the rotation rule

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

• For point \(J(-8,1)\):

Using the rule \((x,y)\to(y, - x)\), we substitute \(x=-8\) and \(y = 1\).
The new coordinates are \((1,8)\).

• For point \(K(-2,1)\):

Substitute \(x=-2\) and \(y = 1\) into the rule \((x,y)\to(y, - x)\).
The new coordinates are \((1,2)\).

• For point \(L(-2,5)\):

Substitute \(x=-2\) and \(y = 5\) into the rule \((x,y)\to(y, - x)\).
The new coordinates are \((5,2)\).

• For point \(M(-8,5)\):

Substitute \(x=-8\) and \(y = 5\) into the rule \((x,y)\to(y, - x)\).
The new coordinates are \((5,8)\).

Answer:

Plot the points \(J'(1,8)\), \(K'(1,2)\), \(L'(5,2)\), \(M'(5,8)\) and connect them to form the rotated square.