Question

Find the value of x for which the distance between the points A(x, 2) and B (9,8) is 10 units

Answer 1

Question :-

• Find the value of x for which the distance between the points A(x, 2)and B (9,8) is 10 units.

Answer :-

• The value of x = 1 or 17

Given :-

• Distance between the points A(x, 2) and B (9,8) is 10 units.

To find :-

• Find the value of x

Solution :-

Given points A(x, 2) and B (9,8) and AB = 10

By using distance formula,

$\boxed {\large\sf AB= \sqrt{ {( x_{2} - x_{1}})^{2} + {( y_{2} - y_{1}) }^{2} } }$

Squaring on both side

$\\ \large\implies\sf {AB}^{2} = {( x_{2} - x_{1}})^{2} + {( y_{2} - y_{1}) }^{2}$

$\\ \large\sf\implies 100 = {(9 - x)}^{2} + {(8 - 2)}^{2}$

$\\ \large\sf\implies100 = {(9 - x)}^{2} + {36}$

$\\ \large\sf \implies100 = 81 + x^2 - 18x + 36$

$\\ \large\sf \implies100 = 117 + x^2 - 18x$

$\\ \large\sf\implies x^2 - 18x + 17 x = 0$

Solving this equation ,

( x - 1 ) ( x - 17 )

x = 1 or x = 17

$\therefore$ The value of x = 1 or 17