Figure W is the result of a transformation on Figure V. Which transformation would accomplish this? x y Figure V Figure W Answer Multiple Choice Answers A translation 2 units left and 5 units up A rotation 90° clockwise about the origin A rotation 90° counterclockwise about the origin A translation 5 units right and 2 units down Submit Answer Copyright ©2026 DeltaMath.com All Rights Reserved. Terms & Policies

Mathematics

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Answer

The transformation that maps Figure V to Figure W is a rotation 90° clockwise about the origin.

Step-by-step solution

3 steps
  1. Identify key points on Figure V.

    Let's pick the top-right vertex of Figure V, which appears to be at coordinates $(2, 4)$.
    Let's also pick the bottom-left vertex, which is at the origin $(0, 0)$.

  2. Identify corresponding points on Figure W.

    The top-right vertex of Figure W (corresponding to (2,4)(2,4) in V) appears to be at coordinates (4,−2)(4, -2).
    The bottom-left vertex of Figure W (corresponding to (0,0)(0,0) in V) is also at the origin (0,0)(0, 0).

  3. Test the transformation options.

    • A translation 2 units left and 5 units up:

      • (x,y)→(x−2,y+5)(x, y) \to (x-2, y+5)
      • (2,4)→(2−2,4+5)=(0,9)(2, 4) \to (2-2, 4+5) = (0, 9). This does not match (4,−2)(4, -2).
      • (0,0)→(0−2,0+5)=(−2,5)(0, 0) \to (0-2, 0+5) = (-2, 5). This does not match (0,0)(0, 0).
    • A rotation 90° clockwise about the origin:

      • The rule for a 90° clockwise rotation about the origin is (x,y)→(y,−x)(x, y) \to (y, -x).
      • Applying this to (2,4)(2, 4): (2,4)→(4,−2)(2, 4) \to (4, -2). This matches the corresponding point in Figure W.
      • Applying this to (0,0)(0, 0): (0,0)→(0,−0)=(0,0)(0, 0) \to (0, -0) = (0, 0). This matches the corresponding point in Figure W.
      • This transformation correctly maps Figure V to Figure W.
    • A rotation 90° counterclockwise about the origin:

      • The rule for a 90° counterclockwise rotation about the origin is (x,y)→(−y,x)(x, y) \to (-y, x).
      • Applying this to (2,4)(2, 4): (2,4)→(−4,2)(2, 4) \to (-4, 2). This does not match (4,−2)(4, -2).
    • A translation 5 units right and 2 units down:

      • (x,y)→(x+5,y−2)(x, y) \to (x+5, y-2)
      • (2,4)→(2+5,4−2)=(7,2)(2, 4) \to (2+5, 4-2) = (7, 2). This does not match (4,−2)(4, -2).
      • (0,0)→(0+5,0−2)=(5,−2)(0, 0) \to (0+5, 0-2) = (5, -2). This does not match (0,0)(0, 0).

    The correct transformation is a rotation 90° clockwise about the origin.

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