Question

1. If the distance between the points (2,-2) and (-1, x) is 5, one of the values of x (d) I (b) 2 (c)-1 (a) -2​

Answer 1

(B) 2 is the correct option

Answer 2

Given : Distance between the points (2, -2) and (-1, x) is 5

To Find : Value of x.

⠀⠀⠀⠀⠀⠀⠀____________________

$\mathfrak {\underline{ \dag \: According \: to \: the \: question \: : }}$

$\:$

$\sf : \implies \: Distance \: = \sqrt{ (x_{2} - x_{1} ) {}^{2} + (y_{2} - y_{1} ) {}^{2} }$

$\:$

$\sf : \implies \: 5 = \sqrt{ ( - 1 - 2) {}^{2} + (x + 2) {}^{2} }$

$\:$

$\sf : \implies \: 5 = \sqrt{( - 3) {}^{2} + (x + 2) {}^{2} }$

$\:$

$\sf : \implies \: (5) {}^{2} = 9 + x + 2$

$\:$

$\sf : \implies \: 25 = x + 11$

$\:$

$\sf : \implies \: x = 25 - 11$

$\:$

$\sf : \implies \: \bold{x = 14}$

$\:$

$\sf\therefore{\underline{Hence, \: the \: value \: of \: x \: is \: \bold{14}.}}$