Question

Find the point on X-axis which is equidistant from A(-3,4)and B(1-4) by using distance formula​

Answer 1

let the point be 'C'

since the point to be found is on x-axis, its coordinates would be

C(x, 0) for some integer 'x'

for it to be equidistant from A(-3, 4) and B(1, -4)

CA = CB

$\sqrt{ {( - 3 - x)}^{2} + {(4 - 0)}^{2} } = \sqrt{ {(1 - x)}^{2} + {( - 4 - 0)}^{2} } \\ \\ squaring \: both \: the \: sides \\ \\ {( - 3 - x)}^{2} + {4}^{2} = {(1 - x)}^{2} + {( - 4)}^{2} \\ { ( - (3 + x))}^{2} + 16 = {(1 - x)}^{2} + 16 \\ {(3 + x)}^{2} = {(1 - x)}^{2} \\ \\ taking \: square \: root \: on \: both \: sides \\ \\ 3 + x = 1 - x \\ x + x = 1 - 3 \\ 2x = - 2 \\ x = - 1$

Hence, the required point is (-1,0)