Question

select the correct answer.

trapezoid klmn is shown in the coordinate grid.

klmn is dilated by a scale factor of 0.5 with the origin as the center of dilation to produce klmn. which figure shows klmn?

Explanation:

Identify the coordinates of the original vertices

$$
LATEXBLOCK0
$$

Apply the dilation scale factor

$$
LATEXBLOCK1
$$

Match with the correct option

• Option 1: Vertices are at \(K'(-1, 2.5)\), \(L'(1, 1.5)\), \(M'(1, -1)\), and \(N'(-1, -1)\) on a grid with unit spacing.
• Option 2: Shows a coordinate system with axes labeled with decimals like \(0.8, 1.6, 2.4\), where the shape is scaled incorrectly.
• Option 3: Shows a larger shape (dilation factor \(> 1\)).
• Option 4: Shows an extremely small shape.
• Therefore, the first graph correctly represents the dilated trapezoid \(K'L'M'N'\).

Answer:

• (A) The first graph, showing the trapezoid with vertices at \(K'(-1, 2.5)\), \(L'(1, 1.5)\), \(M'(1, -1)\), and \(N'(-1, -1)\) on a standard grid. (Correct answer)
• (B) The second graph, showing axes labeled with decimal increments \(0.8, 1.6, 2.4\).
• (C) The third graph, showing an enlarged trapezoid.
• (D) The fourth graph, showing a highly shrunken trapezoid near the origin.