ICSE Class 10 Answered

(i) Since the point (4, 0) and (-3, 0) lie on the x-axis, therefore, they are invariant points under reflection in the x-axis. Hence, line L₁ is the x-axis.

Similarly, points (0, 2) and (0, 3) being the points on the y-axis, line L₂ is the y-axis.

(ii) On reflection in L₁, (x, y) → (x, - y)

      Hence, P(1, 4) → P’ (1, -4) and Q (-3, -5) →  Q’(- 3, 5)

(iii) On reflection in L₂, (x, y) → (-x, y)                                  

      Hence, P(1, 4) → P”(- 1, 4) and Q (- 3, -5) → Q”(3, - 5)

(iv) Given, the transformation

           P’(1, - 4) → P”(- 1, 4) and Q’(- 3, 5) → Q”(3, - 5)

       Hence, mode of transformation is reflection in the origin.