Question

Find distance between the given points: (a+b,a-b) (b-a,a+b)

Answer 1

Answer:

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

Step-by-step explanation:

$Distance \: between \:two \\points \: (x_{1},y_{1}), \:(x_{2},y_{2})\:is ,\\\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

$Now, Here \:given \: two \\points \: are \: (a+b,a-b),\:(b-a,a+b)$

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

Therefore,

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

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Answer 2

Distance between two points $2\sqrt{a^2+b^2}$

Step-by-step explanation:

Given:

Two point:

(a+b,a-b) (b-a,a+b)

Find:

Distance between two points .

Computation:

$Distance = \sqrt{(x2-x1)^2+(y2-y1)^2}\\\\ Distance = \sqrt{[(b-a)-(a+b)]^2+[(a+b)-(a-b)]^2}\\\\ Distance = \sqrt{[-2a]^2+[-2b]^2}\\\\ Distance =\sqrt{4a^2+4b2} \\\\ Distance =2\sqrt{a^2+b^2}$

Distance between two points $2\sqrt{a^2+b^2}$

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https://brainly.in/question/8282322