Question

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

Answer 1

Answer:-

Given points are (3 , a) and (4 , 1).

Distance between the points = √10 units.

We know that,

$Distance \: between \: two \: points = \sqrt{ {( x_{2} - x _{1}) }^{2} + {(y _{2} - y _{1}) }^{2} } \\ \\ → \: \sqrt{10} = \sqrt{ {(4 - 3)}^{2} + {(1 - a)}^{2} } \\ \\ → \sqrt{10} = \sqrt{1 + {(1 - a)}^{2} }$

Square on both sides,

(√10)² = 1 + (1 - a)²

10 = 1 + (1 - a)²

10 - 1 = (1 - a)²

√9 = 1 - a

1 - a = ± 3

- a = (- 3 - 1) or (3 - 1)

a = 4 or - 2.

Hence, the value of a is 4 or - 2.