Question

Find the value of x,if the distance between thr points (x,8) and (4,3) is 13​

Answer 1

Given the points : A(3, 5) and B(x, 8) such that the distance is 5 units:

We will use the distance formula :

AB = sqrt[( xB-xA)^2 + (yB-yA)^2 ]

= sqrt[ ( x -3)^2 + ( 8 - 5)^2]

= sqrt[(x^2 - 6x + 9 + 3^2)

= sqrt(x^2 - 6x + 9 + 9)

= sqrt(x^2 - 6x + 18)

But we know that AB = 5

==> sqrt(x^2 - 6x +....

Given the points : A(3, 5) and B(x, 8) such that the distance is 5 units:

We will use the distance formula :

AB = sqrt[( xB-xA)^2 + (yB-yA)^2 ]

= sqrt[ ( x -3)^2 + ( 8 - 5)^2]

= sqrt[(x^2 - 6x + 9 + 3^2)

= sqrt(x^2 - 6x + 9 + 9)

= sqrt(x^2 - 6x + 18)

But we know that AB = 5

==> sqrt(x^2 - 6x + 18) = 5

Square both sides:

==> x^2 - 6x + 18 = 25

==> x^2 - 6x + 18 -25 = 0

==> x^2 - 6x - 7 = 0

==> We will factor:

==>(x-7) ( x+ 1) = 0

==> x1= 7

==> x2 = -1

Then we have two solutions:

B ( 7,8) OR B(-1, 8)

Answer 2

$\huge\star{\tt{\underline{\underline{\red{Answer\implies16\:or\:-8}}}}}\star$

see the attachment