Question

in the graph below, what is the line of reflection for △xyz and △xyz? a y = 2 b the y - axis c x = 2 d the x - axis

Explanation:

Step1: Recall reflection property

In a reflection, corresponding points of the original and reflected - figure are equidistant from the line of reflection.

Step2: Analyze the x - coordinates

For each pair of corresponding points (e.g., \(X\) and \(X'\), \(Y\) and \(Y'\), \(Z\) and \(Z'\)), the sum of their x - coordinates divided by 2 gives the x - value of the line of reflection. The x - coordinates of corresponding points have the property that if \((x_1,y_1)\) is a point on \(\triangle XYZ\) and \((x_2,y_2)\) is its corresponding point on \(\triangle X'Y'Z'\), the line of reflection \(x = k\) satisfies \(k=\frac{x_1 + x_2}{2}\). For all corresponding points, the line \(x = 2\) is the perpendicular bisector of the line segments connecting corresponding points.

Answer:

C. \(x = 2\)