Question

Q.1) Find a point on x-axis which is equidistant from A(2,-5) and B(-2,9).

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Answer 1

$\huge\color{pink}\boxed{\colorbox{black}{Given,}}$

The points are (2,-5) and (-2,9).

$\huge\color{pink}\boxed{\colorbox{black}{To find,}}$

The point on the x-axis which is equidistant from the two given points.

$\huge\color{pink}\boxed{\colorbox{black}{Solution}}$

Now,the point is on x-axis,so the value 'y' of the given point will be zero.

Let,the value of the 'x' value of the given point = x

[Assume,x as a variable to do the further mathematical calculations.]

$\small \mathsf{ \color{purple}{So,the \: point \: is = (x,0) }}$

As mentioned in the question,the two points are equidistant from (x,0).

So,

Distance between (x,0) and (2,-5)

$\small \mathsf{ \color{pink}{= ✓(x-2)²+(0+5)²}}$

Distance between (x,0) and (-2,9).

$\small \mathsf{ \color{pink}{=✓(x+2)²+(0-9)²}}$

Now,the points are equidistant.

So,

$✓(x-2)²+(0+5)² = ✓(x+2)²+(0-9)² \\(x-2)²+(0+5)² = (x+2)²+(0-9)² \\x²-4x+4+25 = x²+4x+4+81 \\x²-4x-x²-4x = 4+81-4-25 \\-8x = 56 \\x = -7$

$\small \mathsf{ \color{green}{Hence,the \: point \: on \: x-axis \: \: is (-7,0).}}$