Straight Line and Pair of Straight Lines 1 Question 68

68. Two vertices of a triangle are (5,1) and (2,3). If the orthocentre of the triangle is the origin, find the coordinates of the third vertex.

(1978, 3M)

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Answer:

Correct Answer: 68. 7x4y+25=0,4x+7y=11=0,7x4y3=0

Solution:

  1. Let the coordinates of third vertex be C(a,b).

Since, CH is AB,

ba47=14b=7a

Also, AHBC

153b2a=13b=105a

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

a=4,b=7



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