(a) Point P(2, -3) on reflection becomes P'(2, 3). Name the line of reflection (say L₁).

(b) Point P' is reflected to P'' along the line (𝐿₂), which is perpendicular to the line 𝐿₁ and passes through the point, which is invariant along both axes. Write the coordinates of P''.

(c) Name and write the coordinates of the point of intersection of the lines 𝐿₁ and 𝐿₂.

(d) Point P is reflected to P''' on reflection through the point named in the answer of part I of this question. Write the coordinates of P'''. Comment on the location of the points P'' and P'''.

(a) P(2, -3) ⇒ P'(2, 3)

Since, sign of y-coordinate changes.

∴ L₁ = x-axis

Hence, point P becomes P' on reflection in x-axis.

(b) Origin remains invariant on reflection along both the axes.

L₂ is perpendicular to L₁.

It means L₂ is perpendicular to x-axis and passes through (0, 0).

∴ L₂ is y-axis.

P'(2, 3) on reflection in y-axis becomes P''(-2, 3).

Hence, coordinates of P'' = (-2, 3).

(c) x-axis and y-axis intersect at origin.

Hence, coordinates of intersection of lines L₁ and L₂ is (0, 0).

(d) P(2, -3) on reflection in origin becomes P'''(-2, 3).

Since, P'' and P''' have similar co-ordinates.

Hence, P'' and P''' are coincident points.