Assertion (A) : The point (-2, 8) is invariant under reflection in line x = -2

Reason (R) : If a point has its x-coordinate 0, it is invariant under reflection in both axes.

1. Both A and R are correct, and R is the correct explanation for A.

2. Both A and R are correct, and R is not the correct explanation for A.

3. A is true, but R is false.

4. Both A and R are true.

(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'''.

Points (8, 0) and (-3, 0) are invariant points under reflection in the line L₁, points (0, -9) and (0, 5) are invariant points under reflection in the line L₂.

(i) Name or write down equations of the lines L₁ and L₂.

(ii) Write down the images of points P(3, 5) and Q(-8, 3) after reflection in line L₁. Name the images as P' and Q' respectively.

(iii) Write down the images of P and Q on reflection in L₂. Name the images as P" and Q" respectively.

(iv) Describe a single transformation that maps P' to P".

Study the graph and answer each of the following :

(a) Write the coordinates of points A, B, C and D.

(b) Given that, point C is the image of point A. Name and write the equation of the line of reflection.

(c) Write the coordinates of the image of the point D under reflection in y-axis.

(d) What is the name given to a point whose image is the point itself ?

(e) On joining the points A, B, C, D and A in order, a figure is formed. Name the closed figure.