Question

the distance between the points (a,a) and (-√3a,√3a) is
ans - 2√2a units ​

Answer 1

SOLUTION

TO DETERMINE

The distance between the points (a,a) and (-√3a,√3a)

CONCEPT TO BE IMPLEMENTED

For the given two points $\sf{A( x_1 , y_1) \: \: and \: \: B( x_2 , y_2)}$ the distance between the points

$= \sf{ \sqrt{ {(x_2 -x_1 )}^{2} + {(y_2 -y_1 )}^{2} } }$

EVALUATION

Here the given points are (a,a) and (-√3a,√3a)

The distance between the points (a,a) and (-√3a,√3a)

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

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

$\sf = a\sqrt{2 \{ {(1 )}^{2} + {( \sqrt{3}) }^{2} \} }$

$\sf = a\sqrt{ 2(1 + 3) }$

$\sf = a\sqrt{ 2 \times 4 }$

$\sf = 2a\sqrt{ 2 }$

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