Question

If the line segment joining the points (a, b) and ( c, d) subtends a right angle at the origin, then:(A) ac= bd (B) ac =-bd
(C) ab = cd (D) ab=- cd

Answer 1

If the segment joining the points (a,b) and (c,d) subtends a right angle at the origin, then a) ac-bd=0 b) ac+bd=0 c) ab+cd=0 d) ab-cd=0 From Aakash Mathematics coaching material. What's the solution?

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Zafar Hussain, ISB & NIT alumnus

Answered Oct 18, 2015

You can either solve this using vectors as ankit has done. Or use basic coordinate geometry as follows:

Say O (0,0), P(a,b), Q(c,d) are the given points. The information given in the question implies that angle POQ is a right angle.

Conversely lines OP and OQ are perpendicular to each other. Therefore product of their slopes is -1.

We know that slope of a line joining two points (x1,y1) & (x2,y2) is 
(y2-y1)/(x2-x1)

Hence slope of OP = (b-0)/(a-0) = b/a
Similarly slope of OQ =(d-0)/(c-0)=d/c

This (b/a)×(d/c)=-1
That is bd = -ac
That is ac+bd=0

Hope this answer helps

Answer 2

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