Question

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

Answer 1

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Let

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

are two points. The distance between them is given by,

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

Given,

$\begin{gathered}(x_1, y_1) = (a, b) \\ (x_2,y_2) =( - a, - b)\end{gathered}$

So, Distance between them is

$\begin{gathered} = \sqrt{( - a - a) ^{2} + ( - b - b) ^{2} } \\ = \sqrt{( - 2a) ^{2} + { (- 2b)}^{2} } \\ = \sqrt{4 {a}^{2} + 4 {b}^{2} } \\ = \sqrt{4( {a}^{2} + {b}^{2}) } \\ = 2 \sqrt{( {a}^{2} + {b}^{2})} \end{gathered}$