Question

find the point on the x axis which is equal distance from ( 2,-5) (-2,9)
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Answer 1

As the required point line on x-axis so it must be

(x,0).

Now let the point be = P(x,0)

According to given question it is equal distance from

A(2,-5) and B(-2,9).

Now using distance formula

distance b/w A and P

is

$\sqrt{ ({x - 2})^{2} + ( {0 + 5})^{2} } \\ = \sqrt{ {x }^{2} + 4 - 4x + 25} \\ = \sqrt{ {x}^{2} - 4x + 29 } \: \: \: \: .......(i)$

distance b/w B and P is

$\sqrt{( {x + 2})^{2} + ({0 - 9})^{2} } \\ = \sqrt{ {x}^{2} + 4 + + 4x + 81 } \\ = \sqrt{ {x}^{2} + 4x + 85} \: \: \: \: \: ..........(ii)$

according to the question

(i)=(ii)

$\implies \: \sqrt{ {x}^{2} - 4x + 29 } = \sqrt{ {x}^{2} + 4x + 85 } \\ \implies - 4x + 29 = 4x + 85 \\ \implies8x = - 56 \\ \implies \: x = \frac{ - 56}{8} \\ \implies x = - 7$

$coordinates \: of \: point \: P \: are \\ ( - 7,0) \underline {(answer)}$

Answer 2

Answer:

by applying cartesian cordinate formula yu can get the ans.