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On a coordinate plane, a quadrilateral has points E (negative 2, 0), D (0, 4), G (4, 2), and F (0, 0).

Which are true if figure DEFG is reflected across the x-axis? Check all that apply.

D(0, 4) → D'(0, –4)
E(–2, 0) → E'(–2, 0)
The perpendicular distance from G' to the x-axis will equal 2 units.
The perpendicular distance from D' to the x-axis will equal 8 units.
The orientation will be preserved.

1 answer

To analyze the reflections across the x-axis for the points of quadrilateral DEFG, you follow the rule that any point \((x, y)\) when reflected across the x-axis becomes \((x, -y)\). Let's apply this to each point:

  1. Point D(0, 4):

    • After reflecting: D' becomes (0, -4)

  2. Point E(-2, 0):

    • After reflecting: E' becomes (-2, 0) (because the y-coordinate is 0 and remains unchanged)

  3. Point G(4, 2):

    • After reflecting: G' becomes (4, -2)

  4. Point F(0, 0):

    • After reflecting: F' becomes (0, 0) (also unchanged)

Now let's evaluate each statement:

  1. D(0, 4) → D'(0, –4):

    • True: This is correct.

  2. E(–2, 0) → E'(–2, 0):

    • True: This is correct.

  3. The perpendicular distance from G' to the x-axis will equal 2 units:

    • G' is at (4, -2). The distance from G' to the x-axis is the absolute value of the y-coordinate, which is |-2| = 2 units.
    • True: This is correct.

  4. The perpendicular distance from D' to the x-axis will equal 8 units:

    • D' is at (0, -4). The distance from D' to the x-axis is |-4| = 4 units, not 8.
    • False: This is incorrect.

  5. The orientation will be preserved:

    • Reflection across the x-axis does not preserve the orientation of the figure; it flips the orientation.
    • False: This is incorrect.

In summary, the true statements are:

  • D(0, 4) → D'(0, –4)
  • E(–2, 0) → E'(–2, 0)
  • The perpendicular distance from G' to the x-axis will equal 2 units.