Question

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

Answer 1

Given ,

• The distance between the points (x, -1) and (3, 2) is 5 units

We know that , the distance between two points is given by

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

Thus ,

$\sf \mapsto 5 = \sqrt{ {(3 - x)}^{2} + {(2 + 1)}^{2} } \\ \\ \sf squaring \: on \: both \: we \: , \: get \\ \\ 25 = {(3)}^{2} + {(x)}^{2} - 6x + 9 \\ \\ \sf \mapsto 25 = {(x)}^{2} - 6x + 18 \\ \\ \sf \mapsto {(x)}^{2} - 6x - 7 = 0 \\ \\ \sf by \: prime \: factorisation \: method \:, \: we \: get \\ \\ \sf \mapsto {(x)}^{2} + x - 7x - 7 = 0 \\ \\ \sf \mapsto x(x + 1) - 7(x + 1) = 0 \\ \\ \sf \mapsto (x - 7)(x + 1) = 0 \\ \\ \sf \mapsto x = 7 \: \: or \: \: x = - 1$

$\sf \therefore \underline{The \: value \: of \: x \: will \: be \: 7 \: o r -1}$