Question

If the distance between the
points (-1,2) and (x, 6) is 5, One
of the values of 'x' is *​

Answer 1

Step-by-step explanation:

$x_{1} = ( - 1) \: \: \: \: \: \: \: \: \: \: \: y_{1} = 2 \\ x_{2} = x \: \: \ \: \: \: \: \: \: \: \: y_{2} = 6$

Distance=

$\sqrt{( x_{2} - x_{1}) ^{2} + ( y_{2} - y_{1})^{2} }$

$5 = \sqrt{ {( x + 1)}^{2} + (6 - 2) ^{2} } \\ {5}^{2} = {(x + 1)}^{2} + {4}^{2} \\ 25 = {x}^{2} + 1 + 2x + 16 \\ 25 = {x}^{2} + 2x + 17 \\ {x}^{2} + 2x + 17 - 25 = 0 \\ {x}^{2} + 2x - 8 = 0 \\ {x}^{2} + (4 - 2)x - 8 = 0 \\ {x}^{2} + 4x - 2x - 8 = 0 \\ x(x + 4) - 2(x + 4) = 0 \\ (x - 2)(x + 4) = 0 \\ \\ x - 2 = 0 \: \: \: \: \: \: \: \: \:x + 4 = 0 \\ x = 2 \: \: \: \: \: \: \: \: \: x = - 4$

The distance can't be negative ,so x=2

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