Question

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

When a point $(x,y)$ is reflected across the $x - axis$, the transformation is $(x,y)\to(x, - y)$.

Step2: Analyze point D

For point $D(0,4)$, applying the rule $(x,y)\to(x, - y)$, we get $D'(0,-4)$. So, $D(0,4)\to D'(0, - 4)$ is true.

Step3: Analyze point E

For point $E(-2,0)$, applying the rule $(x,y)\to(x, - y)$, we get $E'(-2,0)$ since $0$ remains $0$ when negated. So, $E(-2,0)\to E'(-2,0)$ is true.

Step4: Analyze point G

Assume $G$ has a $y -$coordinate of $2$. After reflection across the $x - axis$, $G'$ has a $y -$coordinate of $- 2$. The perpendicular distance from $G'$ to the $x - axis$ is $| - 2|=2$ units. So, the perpendicular distance from $G'$ to the $x - axis$ will equal 2 units is true.

Step5: Analyze point D'

The perpendicular distance from $D'(0,-4)$ to the $x - axis$ is $| - 4| = 4$ units, not 8 units. So, the perpendicular distance from $D'$ to the $x - axis$ will equal 8 units is false.

Step6: Analyze orientation

Reflection across an axis changes the orientation. So, the orientation will be preserved 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.