Question

Find the distance between the points (a,b) and (-a,- b)

Answer 1

$\huge \underline \mathfrak {Solution:-}$

We have to find out the distance between the two points (a.b) and (-a,-b).

For finding the distance between two points we can use the given formula.

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

This formula is used to find out the distance between two points and that's why it is named as distance formula.

According to question,

$x_1 = a \\ \\ x_2 = -a \\ \\ y_1 = b\\ \\ y_2 = -b$

Now,

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

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

Answer 2

Answer:

here the given points are (a,b) and  (-a,-b).  

let us consider,  

A ( a, b) = ( x1 , y1 )  

B ( - a, - b) = (x2 , y2 )  

we know the distance formula,  

distance = √ [( y2 - y1)² + (x2 - x1)²]  

therefore  

the distance between the points A and B = √ [ (- b - b)² + (-a - a) ²]  

AB = √ [ ( -2b)² + (-2a )² ]  

= √ [ 4b² + 4a² ]

= √ [ 4 ( a ² + b² ) ]  

= 2 √ ( a² + b² )  

therefore the between two given points is 2 √ ( a² + b² )

Explanation:

Thanks.