question_answer

Two points A and B have coordinates (1, 1) and (3, -2) respectively. The co-ordinates of a point distant \[\sqrt{85}\]from B on the line through B perpendicular to AB are                        [AMU 2000]

A) (4, 7)                                         

B) (7, 4)

C) (5, 7)                                         

D) (-5, -3)

Correct Answer: C

Solution :

Trick: From option (c), \[BP=\sqrt{{{(5-3)}^{2}}+{{(7+2)}^{2}}}\]\[=\sqrt{4+81}=\sqrt{85}\]                    Hence option (c) is correct.