Question

Date
find the value of a when the distance
belween the points (3, a) and (4,1)
is √10​

Answer 1

Answer:

$\sqrt{ {(3 - 4)}^{2} + {(a - 1)}^{2} } = \sqrt{10} \\ root \: gets \: cancel \\ { ( - 1)}^{2} + { {a}^{2} - 2(a)(1)} + {(1)}^{2} = 10 \\ 1 + {a }^{2} - 2a + 1 = 10 \\ {a }^{2} - 2a + 2 = 10 \\ {a}^{2} - 2a = 8 \\ {a}^{2} - 2a - 8 \\ middle \: term \: splitting \: \\ sum = ( - 2) ( - 4 + 2)\\ product = ( - 8)( - 4 \times 2) \\ {a}^{2} - 4a - 2a - 8 \\ a(a - 4) - 2(a - 4) \\( a - 4) \: and \: (a - 2) \\ a = 2 \: and \: a = 4$

a can be 2 or 4