Question

trapezoid abcd is the dilation of trapezoid abcd. which algebraic representation shows this dilation? (x, y) --> (3x, 2y) (x, y) --> (0.5x, 0.5y) (x, y) --> (2x, 2y) (2x, 2y) --> (x, y)

Explanation:

Step1: Understand the concept of dilation

Dilation is a transformation that changes the size of a figure. If the scale factor \(k\) is greater than \(1\), the figure is enlarged. For a point \((x,y)\) in a dilation centered at the origin, the new point after dilation is \((kx,ky)\) where \(k\) is the scale factor for both \(x\) and \(y\) - coordinates (assuming uniform dilation in \(x\) and \(y\) directions).

Step2: Analyze the options

• Option \((x,y)\to(3x,2y)\): This is not a uniform dilation (different scale - factors for \(x\) and \(y\)).
• Option \((x,y)\to(0.5x,0.5y)\): This is a reduction (scale factor \(k = 0.5\)).
• Option \((x,y)\to(2x,2y)\): This is a uniform dilation with a scale factor \(k = 2\). If we assume the original trapezoid \(ABCD\) and its dilated image \(A'B'C'D'\) (an enlargement), and for a point \((x,y)\) on \(ABCD\), the corresponding point \((2x,2y)\) on \(A'B'C'D'\) (since in a dilation from the origin, if we double the \(x\) and \(y\) coordinates of each vertex of \(ABCD\), we get \(A'B'C'D'\)).
• Option \((2x,2y)\to(x,y)\): This is a reverse - transformation (from the dilated figure back to the original if the original was dilated by a factor of \(2\)). But the question is about the transformation from \(ABCD\) to \(A'B'C'D'\).

Answer:

\((x,y)\to(2x,2y)\)