Question

If one diagonal of a square is along the line 8x – 15y = 0 and one of its vertex is at (1, 2), then find the equation of sides of the square passing through this vertex.

Answer 1

Let ABCD be the given square and the coordinates of the vertex D be (1, 2). We are required to find the equations of its sides DC and AD.

Given that BD is along the line 8x - 15y = 0, so its slope is 8/15. The angles made by BD with sides AD and DC is 45°. Let the slope of DC be m. Then

or 15 + 8m = 15m – 8

or 7m = 23, which gives m =23/7

Therefore, the equation of the side DC is given by

Similarly, the equation of another side AD is given by