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# if A be(2,2), B be(5,-2) find all points on x-axis such that AP is perpendicular to PB

## 2 Answers

10 years ago

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)

10 years ago

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

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