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If point A(3,5) and B are equidistant from H(√2,√5) and B has rational coordinates then AB = (a) √7 (b) 0 (c) √34 (d) none

If point A(3,5) and B are equidistant from H(√2,√5) and B has rational coordinates then AB =


(a) √7


(b) 0


(c) √34


(d) none

Grade:12

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
Dear student

Let B be (x,y)

Using the fact that the points are equidistant

(x-sqrt(2))^2 + (y-sqrt(5))^2 =(3-sqrt(2))^2 + (5-sqrt(5))^2

we can arrange the equation in the form ((x-3)^2 + (y-5)^2)^0.5

Regards
Vikas TU
14149 Points
3 years ago
The answer is (3,-1).
Let,the coordinates of the required point are=P(x,y).
Distance of AP=Distance of BP
√{(x-5)^2}+{(y-3)^2} = √{(x-5)^2}+{(y+5)^2}
Solving it,we get,y=-1.
Distance of BP=Distance of CP.
√{(x-5)^2}+{(y+5)^2}=√{(x-1)^2}+{(y+5)^2}
Solving this equation we have,x=3.
P=(3,-1)

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