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: Reflection rule

When a point \((x,y)\) is reflected across the \(x -\)axis, the rule is \((x,y)\to(x, - y)\). For point \(D(0,4)\), using the rule \((0,4)\to(0,-4)\). For point \(E(-2,0)\), since \(y = 0\), \((-2,0)\to(-2,0)\) (because \(-0=0\)).

Step2: Perpendicular distance

Let's assume the original \(y -\)coordinate of \(G\) is \(2\). After reflection across the \(x -\)axis, the \(y -\)coordinate of \(G'\) is \(- 2\). The perpendicular distance from a point \((x,y)\) to the \(x -\)axis is \(|y|\). So for \(G'\), \(|y| = |-2|=2\). For \(D'\) with \(y=-4\), the perpendicular distance \(|y|=4
eq8\).

Step3: Orientation

When a figure is reflected across a line (in this case the \(x -\)axis), the orientation of the figure is not preserved (it is flipped). 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.