Question

find the distance between the given points G(a-b) and (-a-b)

Answer 1

SOLUTION

TO DETERMINE

The the distance between the given points (a,b) and (-a, -b)

FORMULA 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,b) and (-a, -b)

Hence the required distance between the points

$\sf{ = \sqrt{ {(a + a)}^{2} + {(b + b)}^{2} } \: \: \: unit }$

$\sf{ = \sqrt{ {(2a )}^{2} + {(2b)}^{2} } \: \: \: unit }$

$\sf{ = \sqrt{ 4{a}^{2} + 4 {b}^{2} } \: \: \: unit }$

$\sf{ = \sqrt{ 4({a}^{2} + {b}^{2}) } \: \: \: unit }$

$\sf{ = 2\sqrt{ {a}^{2} + {b}^{2}} \: \: \: unit }$

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