Q.
P(3, 1), Q(6, 5) and R(x, y) are three points such that the angle RPQ is a right angle and the area of ∆RPQ =7, then the number of such points R is
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a
0
b
1
c
2
d
4
answer is C.
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Detailed Solution
Since the angle RPQ is a right angle,∴ slope of RP × slope of PQ = –1⇒1-y3-x×5-16-3=-1⇒3x+4y=13 (1)Also, area of ∆RPQ = 7⇒12xy1311651=7⇒12x(1-5)-y(3-6)+1(15-6)=±7⇒ – 4x + 3y + 9 = ± 14 ⇒ – 4x + 3y = 5 (2)and – 4x + 3y = –23 (3)Solving Eq. (1) and (2) and (1) and (3), we get twodifferent coordinates of the point R. So, there are two such points R.
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