In a reflection, the image of the line y-2x=3 is the line 2y-x=9.Find the axis of reflection.

Answer 1

Look at the original lines first.
https://www.wolframalpha.com/input/?i=graph+y-2x%3D3%2C+2y-x%3D9

As you can see, there would be two such lines, one will have a positive slope, the other will have a negative slope.
To be on the axis of symmetry, any point (X,Y) must be equidistant from each of the original lines.
Rewriting the origianls as 2x - y + 3 =0 and x - 2y + 9 = 0, and using the "distance from a point to a line" formula, we get
|2X - Y + 3|/√5 = |X - 2Y + 9|/√5
giving us X + Y - 6 = 0 and X - Y + 4 = 0

In terms of the standard (x,y) we have : x + y = 6 and x - y = -4

confirm:
https://www.wolframalpha.com/input/?i=graph+y-2x%3D3%2C+2y-x%3D9%2C+x%2By+%3D+6%2C+x-y+%3D+-4