Question

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

Explanation:

Step1: Find the coordinates of the original kite

From the graph, the coordinates of the vertices of kite \(STUV\) are \(S(0, - 2)\), \(T(1,0)\), \(U(0,2)\), \(V(-1,0)\).

Step2: Apply the dilation formula

The formula for dilation centered at the origin \((x,y)\to(kx,ky)\) where \(k = 4\).
For point \(S(0,-2)\):
\(x = 0,y=-2,k = 4\)
\((0\times4,-2\times4)=(0,-8)\)
For point \(T(1,0)\):
\(x = 1,y = 0,k = 4\)
\((1\times4,0\times4)=(4,0)\)
For point \(U(0,2)\):
\(x = 0,y = 2,k = 4\)
\((0\times4,2\times4)=(0,8)\)
For point \(V(-1,0)\):
\(x=-1,y = 0,k = 4\)
\((-1\times4,0\times4)=(-4,0)\)

Answer:

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