Question

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graph the image of kite abcd after a dilation with a scale factor of 5, centered at the origin.

Explanation:

Step1: Identify the coordinates of the original kite

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

Step2: Apply the dilation formula

For a dilation centered at the origin with scale - factor \(k\), the formula to find the coordinates of the dilated point \((x',y')\) from the original point \((x,y)\) is \((x',y')=(k\cdot x,k\cdot y)\). Here \(k = 5\).
For point \(A(0,-1)\): \(A'(5\times0,5\times(-1))=(0, - 5)\)
For point \(B(2,0)\): \(B'(5\times2,5\times0)=(10,0)\)
For point \(C(0,2)\): \(C'(5\times0,5\times2)=(0,10)\)
For point \(D(-2,0)\): \(D'(5\times(-2),5\times0)=(-10,0)\)

Step3: Graph the new kite

Plot the points \(A'(0, - 5)\), \(B'(10,0)\), \(C'(0,10)\), \(D'(-10,0)\) on the coordinate - plane and connect them in order to form the dilated kite.

Answer:

The new vertices of the dilated kite are \(A'(0, - 5)\), \(B'(10,0)\), \(C'(0,10)\), \(D'(-10,0)\). Graph these points and connect them to get the dilated kite.