Q) Find the ratio in which line y = x divides the line segment joining the points (6, -3) and (1, 6).
Ans: Let’s draw the diagram to solve:
Also consider that the line y = x divided the line PQ in the ratio of m : n.
By section formula, if a point (x, y) divides the line joining the points (x1, y1) and (x2, y2) in the ratio m : n, then coordinates of point R (x, y) =
P (1, 6) = (x1, y1)
Q (6, -3) = (x2, y2)
Since the line PQ is divided in the ratio of m : n, Hence the co-ordinates of point P:
Similarly, y =
Since the point R (x,y) lies on the line y = x, therefore it should satisfy the condition.
∴ (-3 m + 6 n) = (6 m + n)
9 m = 5 n
m : n = 5 : 9
Therefore, the line y = x divides the given line segment in the ratio of 5: 9.