P(3,1)Q(6,5)R(x,y) are 3 points such that the angle RPQ ia right angle then the area of triangle RPQ=7 then the no. Of such points R is.....

Ans. 2

RPQ is a right angle , that surely means that R(x,y) will lie on a line perpendicular to the line joining P(3,1) and Q(6,5) and passes through P.

Since the area of traigle is 7 , since the area of a triangle is (base*height)/2. 

Since the base is given (distance b/w (3,1) and (6,5)) = 5, then height= 14/5= 2.8

Now we know that the points r at distance of 2.8 frm P and perpendicualr to PQ and passes through P,

Two such points are possible intesecting the line perpendicular to PQ and  at distance 2.8. 

    Q(6,5)

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    |5

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R(x1,y1)____2.8___ |P(3.1)__2.8____R(x2,y2)