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

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

Step2: Analyze point D

For point $D(0,4)$, when reflected across the $x -$axis, using the rule $(x,y)\to(x, - y)$, we get $D'(0,-4)$. So the statement $D(0,4)\to D'(0,-4)$ is true.

Step3: Analyze point E

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

Step4: Analyze distance of G'

Assume $G$ has a $y -$coordinate of $2$. When reflected across the $x -$axis, $G'$ has a $y -$coordinate of $- 2$. The perpendicular distance from $G'$ to the $x -$axis is $2$ units. So this statement is true.

Step5: Analyze distance of D'

For $D'(0,-4)$, the perpendicular distance from $D'$ to the $x -$axis is $4$ units, not $8$ units. So this statement is false.

Step6: Analyze orientation

Reflection across the $x -$axis changes the orientation of the figure. So the statement "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.