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

1 thought on “A is a point on x-axis, B = (5, 4) and<br />AB = 5 units, find the co-ordinates of A.​”

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 :-

   [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

   Squaring on both sides :-

   [tex]\implies d^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]

   Solution :-

   [tex]x_1=x,y_1=0[/tex]

   [tex]x_2=5,y_2=4[/tex]

   AB = 5

   Squaring on both sides :-

   [tex](AB)^2=(5)^2[/tex]

   [tex](5-x)^2+(4-0)^2=25[/tex]

   [tex]5^2-10x+x^2+4^2=25[/tex]

   [tex]x^2-10x+25+16-25=0[/tex]

   [tex]x^2-10x+16=0[/tex]

   [tex]x^2-8x-2x+16=0[/tex]

   [tex]x(x-8)-2(x-8)=0[/tex]

   [tex](x-8)(x-2)=0[/tex]

   x = 8 , 2

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

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