Question

find the distance between the points ( a-b, a+b) (a+b a-b)​

Answer 1

Correct Question :

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

$\large{\green{\bold{\underline{To \: Find:}}}}$

Distance between the points.

$\large{\blue{\bold{\underline{Formula \: Used:}}}}$

Distance formula ;

$\sf \: AB = \sqrt{ {(x - x1)}^{2} + {(y - y1)}^{2} }$

$\large{\red{\bold{\underline{Solution:}}}}$

Let the coordinates be :-

A(a-b, a+b) => (x, y)

B(a+b, a-b) => (x1, y1)

Then, on solving further by distance formula

$\sf \: AB = \sqrt{ {(x - x1)}^{2} + {(y - y1)}^{2} } \\ \\ \sf \: AB = \sqrt{ {(a - b- a - b)}^{2} + {(a + b- a + b)}^{2} } \\ \\ \sf \: AB = \sqrt{ {( - 2b)}^{2} + {(2b)}^{2} } \\ \\ \sf \: AB = \sqrt{4 {b}^{2} + 4 {b}^{2} } \\ \\ \sf \: AB = 2 \sqrt{2} b$

$\large{\orange{\bold{\underline{Therefore:}}}}$

The distance between the points is 2√2 b.

Answer 2

$\huge\underline\bold{AnSwEr,}$

Correct Question :

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

$\large{\green{\bold{\underline{To \: Find:}}}}$

Distance between the points.

$\large{\blue{\bold{\underline{Formula \: Used:}}}}$

Distance formula ;

$\sf \: AB = \sqrt{ {(x - x1)}^{2} + {(y - y1)}^{2} }$

$\large{\red{\bold{\underline{Solution:}}}}$

Let the coordinates be :-

A(a-b, a+b) => (x, y)

B(a+b, a-b) => (x1, y1)

Then, on solving further by distance formula

$\sf \: AB = \sqrt{ {(x - x1)}^{2} + {(y - y1)}^{2} } \\ \\ \sf \: AB = \sqrt{ {(a - b- a - b)}^{2} + {(a + b- a + b)}^{2} } \\ \\ \sf \: AB = \sqrt{ {( - 2b)}^{2} + {(2b)}^{2} } \\ \\ \sf \: AB = \sqrt{4 {b}^{2} + 4 {b}^{2} } \\ \\ \sf \: AB = 2 \sqrt{2} b$

$\large{\orange{\bold{\underline{Therefore:}}}}$

The distance between the points is 2√2 b.

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