Question

M and N are two points on the X axis and Y axis respectively. P (3, 2) divides the line segment MN in the ratio 2 : 3.
Find:
(i) the coordinates of M and N
(ii) slope of the line MN.

Answer 1

Let coordinates of M is (a, 0) and M is (0, b).
Point P divides MN in 2 : 3 ratio

`therefore 3 =(3a + 2 xx 0 )/ (3 + 2) " and " 2 =(3xx0+2xx b)/(3+2)`

3a = 15 and 10 = 2b

a = 5 and b = 5 

(i) The coordinates of M is (5, 0) and N(0, 5)
(ii) Slope of the line MN `= (0-5)/(5-0) = -1 `