Question

what is the equation for the line of reflection that maps the trapezoid onto itself?
$y = 2.5$
$y = 4$
$x=-2$
$x = 0$

Explanation:

Step1: Recall the property of line of reflection

A line of reflection that maps a figure onto itself is a line such that for every point \(P\) on the figure, its reflection \(P'\) over the line is also on the figure. For a trapezoid (assuming it is symmetric about a vertical line in this case), we check the \(x -\)coordinates of the corresponding points.

Step2: Analyze the symmetry

Looking at the trapezoid, if we consider the vertical line \(x=- 2\). Let's take a point \((x,y)\) on the trapezoid. The reflection of a point \((x,y)\) over the line \(x = a\) is given by \((2a - x,y)\). If \(a=-2\), for a point \((x_1,y)\) on one - side of the line \(x =-2\), its reflection \((2\times(-2)-x_1,y)=(-4 - x_1,y)\) should also be on the trapezoid.
We can observe that the trapezoid is symmetric about the vertical line \(x=-2\). For example, if we take a point on the left - hand side of \(x =-2\) and find its mirror image across \(x=-2\), the mirror - image point lies on the trapezoid.

Answer:

\(x=-2\)