graph the image of trapezoid stuv after a dilation with a scale factor of 3, centered at the origin.

Answer

Explanation:

Step1: Identify coordinates of vertices

First, find the coordinates of trapezoid ( STUV ):

( S(-3, -3) ) (assuming each grid is 1 unit, from the graph: S is at x=-3, y=-3)
( T(3, -3) ) (T is at x=3, y=-3)
( U(3, 3) ) (U is at x=3, y=3)
( V(-1, 3) ) (V is at x=-1, y=3) Wait, correction: Looking at the graph, V is at (0, 3)? Wait no, the green dots: V is at (0, 3)? Wait the original graph: V is at (0, 3)? Wait no, the user's graph: V is at (0, 3)? Wait no, the x-axis: from -10 to 10, y-axis -10 to 10. Let's recheck:

Looking at the graph:

( S ): x=-3, y=-3 (since it's 3 units left on x, 3 units down on y)
( T ): x=3, y=-3 (3 units right, 3 units down)
( U ): x=3, y=3 (3 units right, 3 units up)
( V ): x=0, y=3 (0 on x, 3 on y) Wait, the green dot for V is at (0, 3), U at (3, 3), T at (3, -3), S at (-3, -3). Yes, that makes sense. So coordinates: ( S(-3, -3) ), ( T(3, -3) ), ( U(3, 3) ), ( V(0, 3) ).

Step2: Apply dilation with scale factor 3, centered at origin

Dilation rule: ((x, y) \to (3x, 3y)) (since scale factor ( k = 3 ), centered at origin).

For ( S(-3, -3) ): ( (3 \times -3, 3 \times -3) = (-9, -9) )
For ( T(3, -3) ): ( (3 \times 3, 3 \times -3) = (9, -9) )
For ( U(3, 3) ): ( (3 \times 3, 3 \times 3) = (9, 9) )
For ( V(0, 3) ): ( (3 \times 0, 3 \times 3) = (0, 9) )

Wait, correction: Wait original V is at (0, 3)? Wait no, in the graph, V is at (0, 3), U at (3, 3), T at (3, -3), S at (-3, -3). Yes. So:

( S(-3, -3) ), ( T(3, -3) ), ( U(3, 3) ), ( V(0, 3) ).

Step3: Dilate each vertex

Dilation with scale factor 3, center at origin: ((x, y) \to (3x, 3y))

( S(-3, -3) ): ( 3 \times -3 = -9 ), ( 3 \times -3 = -9 ) → ( S'(-9, -9) )
( T(3, -3) ): ( 3 \times 3 = 9 ), ( 3 \times -3 = -9 ) → ( T'(9, -9) )
( U(3, 3) ): ( 3 \times 3 = 9 ), ( 3 \times 3 = 9 ) → ( U'(9, 9) )
( V(0, 3) ): ( 3 \times 0 = 0 ), ( 3 \times 3 = 9 ) → ( V'(0, 9) )

Step4: Plot the new vertices

Plot ( S'(-9, -9) ), ( T'(9, -9) ), ( U'(9, 9) ), ( V'(0, 9) ) and connect them to form the dilated trapezoid.

Answer:

The dilated trapezoid ( S'T'U'V' ) has vertices at ( S'(-9, -9) ), ( T'(9, -9) ), ( U'(9, 9) ), ( V'(0, 9) ). To graph it, plot these points and connect ( S' ) to ( T' ) to ( U' ) to ( V' ) to ( S' ).