Question

11. The point on the x-axis which is equidistant from points (-1,0) and
(5,6) is
a) (0,2) b) (2,0) c) (3,0)
d) (0,3)​

Answer 1

Answer:

The point on the X-axis is (5, 0)

Step-by-step explanation:

Let A be the point on X-axis.

Then the co-ordinates of A is (x , 0)

Because y = 0 for X-axis.

Given that- A(x, 0) is equidistant from B(-1, 0) and (5, 6)

Then AB = AC

Using formula-

Distance between two points X(a, b) and Y(c, d) is

XY = $XY = \sqrt{(a-c)^{2}+(b-d)^{2}  }$

We have-

AB = AC

$\sqrt{(x+1)^{2}+(0-0)^{2}  } = \sqrt{(x-5)^{2}+(0-6)^{2}  }$

$\sqrt{x^{2}+1+2x+0 } = \sqrt{x^{2}+25-10x+36 }$

$\sqrt{x^{2}+2x+1 } = \sqrt{x^{2}-10x+61 }$

Squaring on both sides-

$x^{2}+2x+1 = x^{2}-10x+61$

$x^{2} + 2x -x^{2}+10x = 61-1$

12x = 60

$x = \dfrac{60}{12}$

x = 5

A = (x, 0)

A = (5, 0)

Hence, the point on the X-axis is (5, 0)