Question

graph the image of kite abcd after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Find the coordinates of the original kite

The coordinates of the vertices of kite \(ABCD\) are \(A(0, - 2)\), \(B(2,0)\), \(C(0,1)\), \(D(-2,0)\).

Step2: Apply the dilation formula

The formula for dilation centered at the origin \((x,y)\to(kx,ky)\), where \(k = 4\) (scale factor).
For point \(A(0,-2)\):
\(A'(4\times0,4\times(-2))=(0,-8)\)
For point \(B(2,0)\):
\(B'(4\times2,4\times0)=(8,0)\)
For point \(C(0,1)\):
\(C'(4\times0,4\times1)=(0,4)\)
For point \(D(-2,0)\):
\(D'(4\times(-2),4\times0)=(-8,0)\)

Step3: Plot the new points

Plot the points \(A'(0, - 8)\), \(B'(8,0)\), \(C'(0,4)\), \(D'(-8,0)\) on the coordinate - plane and connect them to form the dilated kite.

Answer:

The coordinates of the vertices of the dilated kite are \(A'(0,-8)\), \(B'(8,0)\), \(C'(0,4)\), \(D'(-8,0)\). Plot these points and connect them.