The slopes of two perpendicular lines satisfy which relation?

1. Suppose lines of slopes p and q are perpendicular at point (a, b). 2. Pick (a+1, b+p) on the first line and (a+1, b+q) on the second; these and (a, b) form a right triangle. 3. By Pythagoras: (1² + p²) + (1² + q²) = (q − p)². 4. Simplifying gives 2 + 2pq = 0, hence pq = −1. 5. So the slopes of perpendicular lines multiply to −1. _Source: SCERT Kerala Std X Mathematics Part-2, Chapter 9-11 (pp 227-246, 2019 ed.)._