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indrayani bargaje Grade: 10
        if A be(2,2), B be(5,-2) find all points on x-axis such that AP is perpendicular to PB
6 years ago

Answers : (2)

vikas askiitian expert
510 Points
										

let P is (x,0) then


slope of AP = 2/x-2


slope of PB = 5/-2-x


if lines are perpendicular then product of slopes = -1


(2/x-2) (-5/x+2) = -1


x2 - 4 = 10


x2 = 14


x = +root14 & -root14


points are , (root14,0)  &  (-root14,0)

6 years ago
Thareeq Roshan
31 Points
										

The points are A(2,2) and B(5,-2)


It is given that the point P is in the x-axis therefore lets assume it to be P(x,0)


 


it is also given that AP is perpendicular to BP


therefore if M1   is the slope of AP and M2    is the slope of BP then we know that


               M1 x  M2  = -1


therefore (2-0)/2-x)*(-2-0)/5-x)=-1


you will get a quadratic equation x2-7x+6=0 


 


solving you will get x=1 or x=6


so the point required is P(1,0) or P(6,0)


 


HOPE THAT YOU GOT WHAT YOU NEEDED


BEST OF LUCK FOR YOUR EXAMINATIONS


         

6 years ago
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