Class 10 Optional Mathematics | Combined Transformation of Two Identical Transformation

Activity 1

Method

Study the graph in which point A is reflected in the line x = 0 to give A', and A' is then reflected in the line y = 0 to give A''.
Study the graph in which point B is reflected in the line y = 0 to give B', and B' is then reflected in the line y = 2 to give B''.
Study the graph in which point M is rotated about O to give M', and M' is then rotated about O again to give M''.
Study the graph in which triangle ABC is translated to A'B'C', and A'B'C' is then translated to A''B''C''.
For each graph, answer the questions below and discuss your answers in class.

Discussion

For point A: What are the coordinates of A, A' and A''?
For point A: Reflection in which line gives A' as the image of A?
For point A: Reflection of A' in which line gives A''?
For point A: Do the lines of the two reflections intersect each other or not?
For point A: Which single transformation takes A to A''?
For point B: What are the coordinates of B, B' and B''?
For point B: Reflection in which line gives B' as the image of B?
For point B: Reflection of B' in which line gives B''?
For point B: Are the lines of the two reflections intersecting or parallel?
For point B: Which single transformation takes B to B''?
For point M: What are the coordinates of M, M' and M''?
For point M: About which point, through how many degrees and in which direction is M rotated to give M'?
For point M: About which point, through how many degrees and in which direction is M' rotated to give M''?
For point M: Which single transformation takes M to M''?
For the triangles: What are the coordinates of the vertices of triangles ABC, A'B'C' and A''B''C''?
For the triangles: How many units right and how many units up is ABC moved to give A'B'C'?
For the triangles: How many units right and how many units down is A'B'C' moved to give A''B''C''?
For the triangles: Which single transformation takes ABC to A''B''C''?

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