Question

Find the distance between the points (a,b) , (-a,-b). Pls answer fast with proper explanation.......

Answer 1

Distance formula = √((x1-x2)^2 + (y1-y2)^2)

Here, (x1,y1) = (a,b)

(x2,y2) = (-a,-b)

Distance = √((a+a)^2 + (b+b)^2)

= √(4a^2 + 4b^2)

= 2√a^2+b^2

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

The distance between two points

$( x_1, y_1) \: \: and \: \: ( x_2, y_2 )$is

$\sqrt{ {( x_1 - x_2)}^{2} + { ( y_1 - y_2 )}^{2} } \: \: \: \: \: \: unit$

GIVEN

Two points (a,b) , (-a,-b) are given

TO DETERMINE

The distance between the above two points

EVALUATION

The distance between the points (a,b) , (-a,-b) is

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

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

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

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

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