Find the distance between the origin and the point :

(i) (-8, 6)

(ii) (-5, -12)

(iii) (8, -15)

(i) Since, distance between origin and (x, y) = $\sqrt{x^2 + y^2}$

∴ Distance between origin and the point (-8, 6)

$= \sqrt{(-8)^2 + 6^2}\\[1em] = \sqrt{64 + 36}\\[1em] = \sqrt{100}\\[1em] = \text{10}$

Hence, the distance between the origin and the point (-8, 6) is 10.

(ii) Since, distance between origin and (x, y) = $\sqrt{x^2 + y^2}$

∴ Distance between origin and the point (-5, -12)

$= \sqrt{(-5)^2 + (-12)^2}\\[1em] = \sqrt{25 + 144}\\[1em] = \sqrt{169}\\[1em] = \text{13}$

Hence, the distance between the origin and the point (-5, -12) is 13.

(iii) Since, distance between origin and (x, y) = $\sqrt{x^2 + y^2}$

∴ Distance between origin and the point (8, -15)

$= \sqrt{8^2 + (-15)^2}\\[1em] = \sqrt{64 + 225}\\[1em] = \sqrt{289}\\[1em] = \text{17}$

Hence, the distance between the origin and the point is 17.