Question

graph the image of kite efgh after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Find the coordinates of the original points

From the graph, we can get the coordinates of the vertices of kite \(EFGH\): \(E(-5,1)\), \(F(-1,2)\), \(G(-5,9)\), \(H(-9,2)\)

Step2: Apply the rotation rule

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

• For point \(E(-5,1)\):

After rotation, \(x=-5,y = 1\), the new coordinates are \((-1,-5)\)

• For point \(F(-1,2)\):

After rotation, \(x=-1,y = 2\), the new coordinates are \((-2,-1)\)

• For point \(G(-5,9)\):

After rotation, \(x=-5,y = 9\), the new coordinates are \((-9,-5)\)

• For point \(H(-9,2)\):

After rotation, \(x=-9,y = 2\), the new coordinates are \((-2,-9)\)

Step3: Plot the new points

Plot the points \(E'(-1,-5)\), \(F'(-2,-1)\), \(G'(-9,-5)\), \(H'(-2,-9)\) on the coordinate plane and connect them to form the rotated kite.

Answer:

Plot the points \(E'(-1,-5)\), \(F'(-2,-1)\), \(G'(-9,-5)\), \(H'(-2,-9)\) and connect them.