Question

find the value of a when the distance between the points (a,4) and (1,3) is root 10​

Answer 1

Answer:

$\sqrt{10} = \sqrt{(a-1)^{2} + (4-3)^{2} }$

$10 = (a-1)^{2} + (4-3)^{2}$

$10 = (a-1)^{2} + 1$

$10 = a^{2} - (2)(a)(1) + 1^{2}$

$10 = a^{2} - 2a +1$

$a^{2} - 2a - 9 = 0$

$a = 1 + \sqrt{10} \\a = 1 - \sqrt{10}$

Hope that helped!