Find the value of x if the distance between the points (x, -1) and (3, 2) is 5.

x = 7

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x= -1

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x=5

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None of these

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Solution

The correct options are
A x= -1
B x = 7
Distance between two points $(x_{1}, y_{1})$ and
$(x_{2}, y_{2})$ can be calculated using the
formula $\sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$
Distance between the points $(x, - 1)$ and $(3, 2) = 5$
$=> \sqrt{{(x - 3)}^{2} + {(- 1 - 2)}^{2}} = 5$
$\sqrt{{(x - 3)}^{2} + 9} = 5$
${(x - 3)}^{2} + 9 = 25$
${(x - 3)}^{2} = 16$
$x - 3 = + 4$ or $- 4$
$x = 7$ or $x = - 1$

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