Question

The distance between (a, b), (-a, -b) is :​

Answer 1

Answer:

Step-by-step explanation:

To Find :-

Distance between (a , b) and (-a , -b) :-

Solution :-

Distance Formula :-

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

According to Question :-

x_1 = a , y_1 = b

x_2 = - a , y_2 = - b

Let's do :-

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

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

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

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

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

$= 2\times\sqrt{a^2+b^2}$

$=2\sqrt{a^2+b^2}}$

The distance between (a, b), (-a, -b) is :​ $\sf 2\sqrt{a^2+b^2}$

Answer 2

Given :

• (a, b), (-a, -b)

To find :

• Distance

Solution :

$\sf \sqrt{a {}^{2} + b {}^{2} }$

Distance between two points ( x¹ , y¹ ) and ( x² , y² )

Calculating with Formula

$\sf \sqrt{(x {}^{2} - x {}^{1}) {}^{2} + (y {}^{2} - y {}^{1}) {}^{2} }$

Therefore , the distance between the points (a, b), (-a, -b)

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

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

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