Points (3, 0) and (-1, 0) are invariant points under reflection in the line L1;

points (0, -3) and (0, 1) are invariant points on reflection in line L2.

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

(ii) Write down the images of the points P (3, 4) and Q (-5, -2) on 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) State or describe a single transformation that maps P’ onto p''

#### Solution

(i) We know that every point in a line is invariant under the reflection in the same line.

Since points (3, 0) and (-1, 0) lie on the x-axis.

So, (3, 0) and (-1, 0) are invariant under reflection in x-axis.

Hence, the equation of line L_{1} is y = 0. Similarly, (0, -3) and (0, 1) are invariant under reflection in y-axis. Hence, the equation of line L_{2} is x = 0.

(ii) P’ = Image of P (3, 4) in L_{1} = (3, -4)

Q’ = Image of Q (-5, -2) in L_{1} = (-5, 2)

(iii) P” = Image of P (3, 4) in L_{2} = (-3, 4)

Q” = Image of Q (-5, -2) in L_{2} = (5, -2)

(iv) Single transformation that maps P’ onto P” is reflection in origin.