Straight Line and Pair of Straight Lines 1 Question 8

8. Suppose that the points (h,k),(1,2) and (3,4) lie on the line L1. If a line L2 passing through the points (h,k) and (4,3) is perpendicular to L1, then k/h equals

(a) 17

(b) 13

(c) 3

(d) 0

(2019 Main, 8 April II)

Show Answer

Solution:

  1. Given, points (1,2),(3,4) and (h,k) are lies on line L1, so slope of line L1 is

m1=4231=k2h1m1=12=k2h12(k2)=1(h1)2k4=h+1h+2k=5

and slope of line L2 joining points (h,k) and

(4,3), is m2=3k4h

Since, lines L1 and L2 are perpendicular to each other.

m1m2=1123k4h=1[ from Eqs. (i) and (iii)] 3k=82h2hk=5

On solving Eqs. (ii) and (iv), we get

(h,k)=(3,1) So, kh=31=3



NCERT Chapter Video Solution

Dual Pane