Question

draw the image of the rotation of quadrilateral sort by 270° abo
origin.

Explanation:

Step1: Determine the rotation rule

When rotating a point \((x,y)\) \(270^{\circ}\) counter - clockwise about the origin, the rule is \((x,y)\to(y, - x)\).

Step2: Find the coordinates of the vertices of quadrilateral SORT

Assume the coordinates of \(S=(5,-6)\), \(O = (-2,-1)\), \(R=(-2,3)\), \(T=(5,-2)\).

Step3: Apply the rotation rule to each vertex

• For \(S=(5,-6)\): Using the rule \((x,y)\to(y, - x)\), we get \(S'=(-6,-5)\).
• For \(O=(-2,-1)\): Using the rule \((x,y)\to(y, - x)\), we get \(O'=(-1,2)\).
• For \(R=(-2,3)\): Using the rule \((x,y)\to(y, - x)\), we get \(R'=(3,2)\).
• For \(T=(5,-2)\): Using the rule \((x,y)\to(y, - x)\), we get \(T'=(-2,-5)\).

Step4: Plot the new points and draw the quadrilateral

Plot the points \(S'(-6,-5)\), \(O'(-1,2)\), \(R'(3,2)\), \(T'(-2,-5)\) on the coordinate plane and connect them in order to form the rotated quadrilateral.

Answer:

The image of the rotated quadrilateral is formed by the points \(S'(-6,-5)\), \(O'(-1,2)\), \(R'(3,2)\), \(T'(-2,-5)\) connected in order.