InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Point P divides the lne segment joning the points A (2,1) and `B(5,-8)` such that `(AP)/(AB)=1/3` . If P lies on the line ` 2x - y + k = 0 ,` find the value of k |
|
Answer» Correct Answer - Values of k is -8 `(AP)/(AB) = 1/3` ` :. 3 AP = AB` ` 3AP - AP = PB " " …(A-P-B)` ` :. 2AP = PB` ` (AP)/(PB) = 1/2` ` :. ` P divides the segment AB in the ratio AP : PB i.e 1:2 A (2,1) and B `(5,-8)` Let `A(x_(1),y_(1))and B (x_(2),y_(2)) and P (x,y)` ` :. x_(1) = 2 , y_(1) = 1 , x_(2) = 5 and y_(2) = -8` ` m : n = 1 :2` By section formula , ` x = (mx_(2)+nx_(1))/ (m+n) " " and y = (my_(2)+ny_(1))/(m+n)` ` :. x = (1(5)+2(2))/(1+2) " " :. y = (1(-8)+2(1))/(1+2)` ` :. x = 9/3 " " :. y = (-6)/3 ` ` :. x = 3 " " :. y = -2` ` :. ` the coordinates of point P will be `(3,-2)` `P (3,-2) " lies on the line " 2x - y + k = 0` ` :. ` its coordinates satisfy the equation of the line substituting x = 3 and ` y = -2 "in " 2x - y +k = 0,` we get ` 2(3) -(-2) +k =0` ` :. 6+ 2+ k =0` ` :. 8+k = 0` ` :. k = -8` |
|