Question

Write the coordinate of a point p on x- axis which is equidistant from the points a (-2,0) and b(6,0) 0

Answer 1

The point p on x- axis which is equidistant from the points a (-2,0) and b(6,0) is (2,0).

Explanation:

Let the coordinates of point P be (x,0).

If point p on x- axis which is equidistant from the points a (-2,0) and b(6,0).

Then , $PA=PB$

By Using distance formula ,

$\sqrt{(x-(-2))^2+(0-0)^2}=\sqrt{(x-6)^2+(0-0)^2}\\\\\Rihgtarrow\ \sqrt{(x+2)^2}=\sqrt{(x-6)^2}\\\\ \Rihgtarrow\ \sqrt{x^2+4+4x}=\sqrt{x^2+36-12x}\\\\\Rihgtarrow\ x^2+4+4x=x^2+36-12x\\\\\Rightarrow\ 4+4x=36-12x\\\\\Rightarrow\ 4x+12x=36-4\\\\\Rightarrow\ 16x=32\\\\\Rightarrow\ x=\dfrac{32}{16}=2$

Hence, the point p on x- axis which is equidistant from the points a (-2,0) and b(6,0) is (2,0).

# Learn more :

If the points (-2,-1) (1,0) (x, 3) (3, y)

form a parallelogram. Find x & y,​

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Answer 2

Answer:

(2,0) is the answer. solution in attachment.