Question

The point on the axis which is equidistant from points (-1,0) and (5,0) is

Answer 1

The value of x ias "2".

Step-by-step explanation:

Let P(x, 0) be the equidistance from  points A(-1,0) and B(5,0).

∴ $PA^{2}$ = $PB^{2}$

Using distance formula,

$(x_2 - x_1) ^{2}$ + $(y_2 - y_1) ^{2}$

⇒ $(- 1 - x) ^{2}$ + $(0 - 0) ^{2}$  = $(5 - x) ^{2}$ + $(0 - 0) ^{2}$

⇒ $(- 1 - x) ^{2}$ = $(5 - x) ^{2}$

⇒ 1 + 2x + $x^{2}$ = 25 - 10x + $x^{2}$

⇒ 1 + 2x = 25 - 10x

⇒ 2x + 12x = 25 - 1 = 24

⇒ x = 2

Hence, the value of x ias "2".