Question

Find the distance between the following pair of points:
(a, b), (- a, - b)

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

We know that,

$\Large{\implies{\boxed{\boxed{\sf{Distanve = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}}}}}$

Where,

• x1 = a
• x2 = -a
• y1 = b
• y2 = -b

_____________[Put Values]

$\sf{→ Distance = \sqrt{(-a -a )^2 + (-b -b )^2}} \\ \\ \sf{→ Distance = \sqrt{(-2a)^2 + (-2b)^2}} \\ \\ \sf{→ Distance = \sqrt{4a^2 + 4b^2}} \\ \\ \sf{→ Distance = \sqrt{4(a^2 + b^2)}} \\ \\ \sf{→ Distance = \sqrt{(2)^2 \times (a^2 + b^2)}} \\ \\ \sf{→ Distance = 2 \sqrt{a^2 + b^2}}\\ \\ \Large{\implies{\boxed{\boxed{\sf{Distance = 2 \sqrt{(a^2 + b^2)}}}}}}$