Question

analyzing statements about a reflection
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.

Explanation:

Step1: Recall reflection rule across x - axis

When a point $(x,y)$ is reflected across the x - axis, the transformation is $(x,y)\to(x, - y)$.
For point D(0,4), when reflected across the x - axis, D(0,4)→D(0, - 4), so the first statement is true.
For point E(-2,0), when reflected across the x - axis, E(-2,0)→E(-2,0) since $y = 0$ and $-y=0$, so the second statement is true.

Step2: Analyze perpendicular distances

The y - coordinate of a point gives the perpendicular distance from the point to the x - axis. For point G, assume its coordinates are (4,2). After reflection across the x - axis, G'(4, - 2). The perpendicular distance from G' to the x - axis is 2 units, so the third statement is true.
For point D, after reflection D'(0, - 4), the perpendicular distance from D' to the x - axis is 4 units, not 8 units, so the fourth statement is false.

Step3: Analyze orientation

When a figure is reflected, the orientation changes. For example, a right - hand oriented figure will become left - hand oriented after reflection, so the fifth statement is false.

Answer:

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.