Question

If the distance between the points (x, – 1) and (3, 2) is 5, one of the values
of x is -------​

Answer 1

$Let \: A(x,-1) = (x_{1} , y_{1}) \:and \: B(3,2) \:are$

$two \: points$

/* Distance Formula: */

$\boxed{\pink{ Distance = \sqrt{ (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }}}$

$Here, x_{1} = x , y_{1} = -1 , x_{2} = 3, y_{2} = 2$

$Distance (AB) = 5 \: \blue {(given )}$

$\implies AB^{2} = 5^{2}$

$\implies ( 3 -x)^{2} + [ 2-(-1)]^{2} } = 25$

$\implies ( 3 -x)^{2} + 3^{2} = 25$

$\implies ( 3 -x)^{2} = 25 - 9$

$\implies ( x - 3)^{2} = 16$

$\implies x - 3 = \pm \sqrt{16}$

$\implies x = 3 \pm 4$

$\implies x = 3 + 4 \: or \:x = 3 - 4$

$\implies x = 7 \: Or \: x = -1$

/* x should not be negative */

Therefore.,

$\red{ Value \:of \: x } \green { = 7 }$

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