Question

The distance between A(a+b , a-b) and B(b-a , b+a) is

Answer 1

Answer:

AB = √4 ( a^2 - b^2 ) = 2√( a^2 - b^2)

Step-by-step explanation:

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Answer 2

★GIVEN:-

• A(a+b , a-b)

• B(b-a , b+a)

★find:-

• distance between A and B

★solution:-

• we know that A and B distance formula

$\implies \red{AB} = \pink{ \sqrt{( x_{1} - x_{2} ) {}^{2} + ( y_{1} - y_{2}) {}^{2} } }$

where

$\implies \red {x_{1} =a + b } \: \: \: \: \implies \pink{ y_{1} = a - b } \\ \\ \implies \red{ x_{2} = b - a } \: \: \: \: \: \: \: \implies \: \pink{ y_{2} = b + a}$

now applied two point distance formula

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

we know that formula of

$\implies \star \pink{(a + b) {}^{2} = a {}^{2} + b {}^{2} + 2ab } \\ \\ \implies \star \pink{ (a - b) {}^{2} = a {}^{2} + b {}^{2} - 2ab }$

$\implies \: \sqrt{a {}^{2} + b {}^{2} + 2ab - (a {}^{2} + b {}^{2} - 2ab) + (b {}^{2} + a {}^{2} - 2ba) - (b {}^{2} + a {}^{2} + 2ba }$

$\implies \: \sqrt{a {}^{2} + b {}^{2} + 2ab - a {}^{2} - b {}^{2} + 2ab + b {}^{2} + a {}^{2} - 2ba - b {}^{2} - a {}^{2} - 2ba } \\ \\ \\ \implies \: \sqrt{4ab - 4ab} \\ \\ \implies = 0$

answer

The distance between A(a+b , a-b) and B(b-a , b+a) is=

$\implies \pink{0}$

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