Question

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Explanation:

To determine the correct transformation (translation) of the rectangle \(ABCD\) to \(A'B'C'D'\), we analyze the horizontal and vertical shifts:

Step 1: Identify Coordinates (Example: Point \(A\) and \(A'\))

• For Rectangle \(ABCD\) (original): Let’s assume \(A\) has coordinates \((x_1, y_1)\).
• For Rectangle \(A'B'C'D'\) (image): \(A'\) has coordinates \((x_2, y_2)\).

Step 2: Analyze Horizontal (x-axis) and Vertical (y-axis) Shifts

• Option B: The original rectangle \(ABCD\) (with \(A\) at \((2,9)\), \(B\) at \((4,9)\), \(C\) at \((4,5)\), \(D\) at \((2,5)\)) translates horizontally to the right (x increases) and vertically no change (y remains same). The image \(A'B'C'D'\) has \(A'\) at \((6,9)\), \(B'\) at \((8,9)\), \(C'\) at \((8,5)\), \(D'\) at \((6,5)\). This is a horizontal translation (no vertical shift), preserving the shape and size (translation is a rigid transformation).

• Option A: The image is stretched (not a translation, as dimensions change).
• Option C: The vertical position changes (y-coordinate shifts), which is inconsistent with a pure horizontal translation.
• Option D: The image is rotated/reflected (not a translation, as orientation changes).

Answer:

B (the rectangle in Option B shows a horizontal translation of \(ABCD\) to \(A'B'C'D'\) with no vertical shift and preserved dimensions)