Question

given (\triangle abc) and its reflection image (\triangle abc) find the line of reflection.
draw the line of reflection on the graph on the right

Explanation:

Step1: Find the mid - points of corresponding points

Let's assume the coordinates of \(A\), \(B\), \(C\) and \(A'\), \(B'\), \(C'\). For a point \(P(x,y)\) and its reflection \(P'(x',y')\) over a line \(l\), the line \(l\) is the perpendicular bisector of the segment \(PP'\).
Take two corresponding points, say \(A\) and \(A'\). Let \(A=(x_1,y_1)\) and \(A'=(x_2,y_2)\). The mid - point \(M\) of \(AA'\) has coordinates \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Do the same for another pair of corresponding points (e.g., \(B\) and \(B'\)).

Step2: Determine the line

If we assume (by counting the grid squares) that the mid - points of all corresponding points (e.g., \(AA'\), \(BB'\), \(CC'\)) lie on the line \(x = 6\) (by observing the horizontal position of the mid - points of the segments joining corresponding vertices of \(\triangle ABC\) and \(\triangle A'B'C'\) on the grid).

Answer:

The line of reflection is \(x = 6\)