InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Suppose that the points `(h,k)`, `(1,2)` and `(-3,4)` lie on the line `L_(1)`. If a line `L_(2)` passing through the points `(h,k)` and `(4,3)` is perpendicular to `L_(1)`, then `k//h` equalsA. `-(1)/(7)`B. `(1)/(3)`C. `3`D. `0` |
|
Answer» Given points are `P(1,2)`, `(-3,4)` and `(h,k)` are lies on line `L_(1)`, so slope of line `L_(1)` is `m_(1)=(4-2)/(-3-1)=(k-2)/(h-1)` `impliesm_(1)=(-1)/(2)=(k-2)/(h-1)`……..`(i)` `implies 2(k-2)=-1(h-1)` `implies2k-4=-h+1` `impliesh+2k=5`……..`(ii)` and slope of line `L_(2)` joining points `(h,k)` and `(4,3)`, is `m_(2)=(3-k)/(4-h)`........`(iii)` Since, lines `L_(1)` and `L_(2)` are perpendicular to each other. `impliesm_(1)m_(2)=-1` `implies(-(1)/(2))((3-k)/(4-h))=-1` [from Eqs. `(i)` and `(iii)`] `implies3-k=8-2h` `implies2h-k-5`.....`(iv)` On solving Eqs. `(ii)` and `(iv)`, we get `(h,k)=(3,1)` So, `(k)/(h)=(3)/(1)=3` |
|