Question

graph the image of rhombus abcd after a rotation 270° counterclockwise around the origin.

Explanation:

Step1: Determine the rotation rule

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

Step2: Find the coordinates of the original points

Assume \(A(0,-7)\), \(B(5,-7)\), \(C(9,-3)\), \(D(5,-3)\).

Step3: Apply the rotation rule

For point \(A(0,-7)\):
Using the rule \((x,y)\to(y, - x)\), when \(x = 0\) and \(y=-7\), the new coordinates are \(A'(-7,0)\).
For point \(B(5,-7)\):
When \(x = 5\) and \(y=-7\), the new coordinates are \(B'(-7,-5)\).
For point \(C(9,-3)\):
When \(x = 9\) and \(y=-3\), the new coordinates are \(C'(-3,-9)\).
For point \(D(5,-3)\):
When \(x = 5\) and \(y=-3\), the new coordinates are \(D'(-3,-5)\).

Step4: Plot the new points

Plot the points \(A'(-7,0)\), \(B'(-7,-5)\), \(C'(-3,-9)\), \(D'(-3,-5)\) on the coordinate plane and connect them to form the rotated rhombus.

Answer:

Plot the points \(A'(-7,0)\), \(B'(-7,-5)\), \(C'(-3,-9)\), \(D'(-3,-5)\) and connect them.