Find the distance between the following pair of points :

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

By distance formula,

d = $\sqrt{(x$2 - x1)^2 + (y2 - y1)^2}

Let P(x₁, y₁) and Q(x₂, y₂) be the given points

Co-ordinates of P = (a, b)

Co-ordinates of Q = (-a, -b)

$PQ = \sqrt{(-a - a)^2 + (-b - b)^2} \\[1em] = \sqrt{(-2a)^2 + (-2b)^2} \\[1em] = \sqrt{4a^2 + 4b^2}\\[1em] = \sqrt{4(a^2 + b^2)} \\[1em] = 2\sqrt{a^2 + b^2}.$

Hence, distance between (a, b) and (-a, -b) = $2\sqrt{a^2 + b^2}$ units.