Question

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

Explanation:

Step1: Identify original coordinates

Let's assume the coordinates of the vertices of kite \(ABCD\) are \(A(0, - 2)\), \(B(2,0)\), \(C(0,1)\), \(D(-2,0)\) (by observing the graph).

Step2: Apply dilation formula

The formula for dilation centered at the origin with scale - factor \(k\) is \((x,y)\to(kx,ky)\). Here \(k = 4\).
For point \(A(0,-2)\): \((0\times4,-2\times4)=(0,-8)\)
For point \(B(2,0)\): \((2\times4,0\times4)=(8,0)\)
For point \(C(0,1)\): \((0\times4,1\times4)=(0,4)\)
For point \(D(-2,0)\): \((-2\times4,0\times4)=(-8,0)\)

Step3: Graph new points

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

Answer:

Plot the points \((0,-8)\), \((8,0)\), \((0,4)\), \((-8,0)\) and connect them to get the dilated kite.