Question

Assuming that the straight lines work as a plane mirror for a point find the image of the point (1,2) in the line x- 3y + 4 = 0

Answer 1

Let(h , k) be image of the point (x1 , y1) to the straight line ax + by + c = 0 then

( h - x1) / a = ( k - y1) /b =
-2( ax1 + by1 + c) / a2 + b2 .

Here (x1 , y1) = (1,2) and
ax + by + c = 0 is x - 3y + 4 = 0 .

( h - 1) / 1 = ( k - 2) / -3 =
-2( 1 - 6 +4) / (1 + 9)

( h - 1) / 1 = ( k - 2) / -3 =
-2( -1) / 10

( h - 1) / 1 = ( k - 2) / -3 = 1 / 5

∴ ( h - 1) / 1 = 1 / 5 and
( k - 2) / -3 = 1 / 5

5h - 5 = 1 and 5k - 10 = -3

h = 6 / 5 and 5k = 7

h = 6 / 5 and k = 7/5

the image of the point =
( 6/5 , 7/5)