Question

given △abc and its reflection image △abc find the line of reflection. draw the line of reflection on the graph on the right. click to enlarge graph

Explanation:

Step1: Identify mid - points of corresponding points

For each pair of corresponding points (e.g., A and A', B and B', C and C'), find the mid - point. The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Determine the line

The line of reflection is the line that passes through the mid - points of all corresponding points. By observing the mid - points of the corresponding vertices of $\triangle ABC$ and $\triangle A'B'C'$, we find that the line of reflection is the vertical line $x = 4$.

Answer:

The line of reflection is $x = 4$.