Question

find the distance between (a,a) and (-√3a,√3a)
IT'S URGENT PLS FAST

Answer 1

Please see the attachment

Answer 2

Answer:

The distance between (a,a) and (-√3a,√3a) is $2a \sqrt{2}$unit.

Step-by-step explanation:

Given two points are (a,a) and (-√3a,√3a) .

We want to find distance between these two points.

But now question is How can we find distance between two points ?

Let (p,q) and (s,t) be two points

Then distance between them $= \sqrt{ {(p - s)}^{2} + {(q - t)}^{2} }$unit.

Here

$(p,q) = (a,a)$

and $(s,t) = ( - \sqrt{3} a, \sqrt{3} a)$

Now distance between (a,a) and (-√3a,√3a)

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

$=\sqrt{ {a}^{2} + 2 \times a \times \sqrt{3} a + { \sqrt{3}a }^{2} + {a}^{2} - 2 \times a \times \sqrt{3} a } + {( \sqrt{3} a})^{2}$

$= \sqrt{ {a}^{2} - 2 \sqrt{3} {a}^{2} + 3 {a}^{2} + {a}^{2} + 2 \sqrt{3} {a}^{2} + 3 {a}^{2} }$

$= \sqrt{{a}^{2}+3 {a}^{2} + {a}^{2}+3 {a}^{2} } \\ = \sqrt{8 {a}^{2} } \\ = 2a \sqrt{2}$unit.

Required distance is $2a \sqrt{2}$unit.