Question

The point on the x-axis which is equidistant from (-4,0) and (10, 0) is
(A)
(B)
C)
(7,0)
(5,0)
(0,0)
DY (3,0)​

Answer 1

#RamRam ji.................

Answer 2

Option D = (3, 0)

Step-by-step explanation:

Let the point on the x-axis be (p, 0).

Then the distance of (p, 0) from the point (- 4, 0) is

= √{(p + 4)² + (0 - 0)²} units

= √{(p + 4)²} units

= √(p² + 8p + 16) units

and the distance of (p, 0) from the point (10, 0) is

= √{(p - 10)² + (0 - 0)²} units

= √{(p - 10)²} units

= √(p² - 20p + 100) units

By the given condition,

√(p² + 8p + 16) = √(p² - 20p + 100)

or, p² + 8p + 16 = p² - 20p + 100

or, 8p + 16 = - 20p + 100

or, 28p = 84

or, p = 3

∴ the required point on the x-axis is (3, 0).

Equidistance related problem:

If the point R(x,y) is equidistant from two points P (-3, 4) and Q (2, -1), prove that y = x + 2. - https://brainly.in/question/13073351