Question

A is a point on x-axis, B = (5, 4) and
AB = 5 units, find the co-ordinates of A.​

Answer 1

Answer:

(8 , 0) (or) (2 , 0)

Step-by-step explanation:

Given,

B = (5 , 4)

As 'A' is the point on 'x' axis the co-ordinates of 'A' will be "(x , 0)"

AB = 5units

To Find :-

Co-ordinates of point 'A'

Formula Required :-

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Squaring on both sides :-

$\implies d^2=(x_2-x_1)^2+(y_2-y_1)^2$

Solution :-

$x_1=x,y_1=0$

$x_2=5,y_2=4$

AB = 5

Squaring on both sides :-

$(AB)^2=(5)^2$

$(5-x)^2+(4-0)^2=25$

$5^2-10x+x^2+4^2=25$

$x^2-10x+25+16-25=0$

$x^2-10x+16=0$

$x^2-8x-2x+16=0$

$x(x-8)-2(x-8)=0$

$(x-8)(x-2)=0$

x = 8 , 2

Co-ordinates of A = (x , 0) = (8 , 0) (or) (2 , 0)