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.