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.

Answer:

A,B,C

Step-by-step explanation:

If figure DEFG is reflected across the x-axis, the correct statements are:

D(0, 4) → D'(0, –4)

E(–2, 0) → E'(–2, 0)

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

Options A, B, and E are the correct answers.

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

D(0, 4) → D'(0, –4) - True.

Reflecting a point across the x-axis negates its y-coordinate.

E(–2, 0) → E'(–2, 0) - True.

Reflecting a point across the x-axis does not change its x-coordinate.

The perpendicular distance from G' to the x-axis will equal 2 units. - False. The perpendicular distance from G' to the x-axis will be the same as the perpendicular distance from G to the x-axis.

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

The perpendicular distance from D' to the x-axis will be the same as the perpendicular distance from D to the x-axis, which is twice the distance between D and the x-axis.

The orientation will be preserved. - False.

Reflecting a figure across the x-axis will reverse the orientation of the figure.

Thus,

D(0, 4) → D'(0, –4) - True

E(–2, 0) → E'(–2, 0) - True

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

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