Question

Find the distance between the following pairs of point.
(a + b, b + c), (a - b, c-b)
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Answer 1

Answer:

Distance formula - distance between two points ( a$_1$,b$_1$) and ( a$_2$, b$_2$)

Here,

Points are ( a + b , b + c ) and ( a - b, c - b )

Using distance formula -

$\implies\sqrt{(a+b-(a-b))^2+(b+c-(c-b))^2}\\\\\implies\sqrt{(a+b-a+b)^2+(b+c-c+b)^2}\\\\\implies\sqrt{(2b)^2+(2b)^2)}\\\\\implies\sqrt{2^2(b^2+b^2)}\\\\\implies 2\sqrt{b^2+b^2}\\\\\implies2b\sqrt2$

Hence, distance between these points is 2b$\sqrt{2}$.

Answer 2

Answer :

Let the points be A and B.

Given that, A (a + b, b + c).

And, B (a - b, c - b).

Distance Formula : √{(x1 - x2)² + (y1 - y2)²}

⇒ √[{(a + b) - (a - b)}² + {(b + c) - (c - b)}²]

⇒ √[{a + b - a + b}² + {b + c - c + b}²]

⇒ √[{2b}² + {2b}²]

⇒ √[4b² + 4b²]

⇒ √[8b²]

⇒ √[2 × 2 × 2 × b²]

⇒ 2b√2

Hence, Distance between the given two points (A and B) is 2b√2 units.