Question

If the distance between the points A(2,-2) and B(-1,x)
is equal to 5 then value of x is .
(a)2
(b)-2
(c)1
(d)-1 ​

Answer 1

Answer:

here is your answer

match it

thanks

Answer 2

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

$B(-1,x) = ( x_{2} , y_{2})$

$Given \: AB = 5$

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

$\implies (x_{2} - x_{1})^{2} + (y_{2}-y_{1})^{2}=25$

$\blue{ ( By \: Distance \:formula . ) }$

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

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

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

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

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

$\implies (x+2)= \pm \sqrt{16 }$

$\implies x + 2 = \pm 4$

$\implies x = -2 \pm 4$

$\implies x = -2 + 4 \:or \: x = -2 - 4$

$\implies x = 2 \:or \: x = -6$

Therefore.,

$\green { x = 2 \:or \: x = -6}$

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