Question

Find the value of a whend the distance between the points (3,a) and (4,1) is root 10

Answer 1

➡HERE IS YOUR ANSWER⬇

Given that, the distance between the points (3,a) and (4,1) is root(10) units.

Then,

$\sqrt{ {(3 - 4)}^{2} + {(a - 1)}^{2} } = \sqrt{10} \\ \\ squaring \: \: both \: \: sides \: \: we \: \: get \\ \\ or \: \: 1 + {(a - 1)}^{2} = 10 \\ \\ or \: \: {(a - 1)}^{2} = 9 \\ \\ or \: \: {(a - 1)}^{2} - {3}^{2} = 0 \\ \\ or \: \: (a - 4)(a + 2) = 0\\ \\ hence \: \: a = 4 \: \:and \: \: a = - 2$

⬆HOPE THIS HELPS YOU⬅