Question

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

Answer 1

The distance between the points (a, b) and (-a, b) is $2 \sqrt{\left(a^{2}+b^{2}\right)} \text { units }$

Solution:

Given, two points are (a, b) and (- a, - b)

We need to find the distance between above two points.

We know that, distance between two points $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ is given by:

$D(P, Q)=\sqrt{\left(x_{2}-x_{1}\right)^{2}-\left(y_{2}-y_{1}\right)^{2}}$

$\text { here, } x_{2}=-a, y_{2}=-b, x_{1}=a \text { and } y_{1}=b$

$\text { Now, distance }=\sqrt{(a-(-a))^{2}+(b-(-b))^{2}}$

$\begin{array}{l}{=\sqrt{(a+a)^{2}+(b+b)^{2}}} \\\\ {=\sqrt{(2 a)^{2}+(2 b)^{2}}=\sqrt{4\left(a^{2}+b^{2}\right)}} \\\\ {\text { Distance }=2 \sqrt{\left(a^{2}+b^{2}\right)}}\end{array}$

Hence, the distance between two points is $2 \sqrt{\left(a^{2}+b^{2}\right)} \text { units }$

Answer 2

Answer:

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

Step-by-step explanation:

$Distance\: between \: the \: points \\</p><p>(x_{1},y_{1})\:and\: (x_{2},y_{2})\\= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

$Here,\:x_{1} = a , \: y_{1}= b;\\</p><p> x_{2} = - a , \: y_{2}= -b$

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

Therefore.,

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

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