Question

Point (0,3) is an invariant point under the reflection in the line L. Name and write equation of the line L​​

Answer 1

Step-by-step explanation:

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

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

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

Therefore, the equation of line L

1

is y=0.

Similarly, (0,−3) and (0,1) are also invariant under reflection in y-axis.

Therefore, the equation of line L

2

is x=0.

(ii) P' = Image of P(3,4) in L

1

=(3,−4)

And, Q' = Image of Q(−5,−2) in L

1

=(−5,2)

(iii) P'' = Image of P(3,4) in L

2

=(−3,4)

And, Q'' = Image of Q(−5,2) in L

2

=(5,−2)

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