Column-I Column- II (A) Two vertices of a triangle are  and . If orthocentre of the third vertex are (p) (B) A point on the line  which lies at a unit distance from the line  is (q) (C) Orthocentre of the triangle formed by the lines  is (r) (D) If  are in A.P., then lines  are concurrent at (s) CODES :   A B C D     a) P q s r     b) t r s p     c) q p r t     d) s p q r

Question ID - 55399 :- Column-I Column- II (A) Two vertices of a triangle are  and . If orthocentre of the third vertex are (p) (B) A point on the line  which lies at a unit distance from the line  is (q) (C) Orthocentre of the triangle formed by the lines  is (r) (D) If  are in A.P., then lines  are concurrent at (s) CODES :   A B C D     a) P q s r     b) t r s p     c) q p r t     d) s p q r

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(a)

1.

(i)

(ii)

Hence, point, is

1.    (i)

(ii)

Let  be the point on (i). Then,

Hence, the required point is either (3, 1) or

2. Since lines  and  are perpendicular, orthocentre of the triangle is the point of intersection of these lines, i.e,

3. Since,  are in A.P., so

Comparing with the line , we have  and . Hence, lines are concurrent at

Next Question :
 Column-I Column- II (A) If lines  and  are concurrent, then value of  is (p) (B) If the points  and  are collinear, then the value of  is (q) (C) If line , passing through the intersection of  and , is perpendicular to one of them, then the value of  is (r) 4 (D) If line  is equidistant from the points  and (3, 4) then  is (s) 2 CODES : A B C D a) P,q q s,t r b) s,p q,r t q c) s t,s q p,q d) p,s q,s p,r s