Question

What is the distance from the origin (0,0) to the point (34,-78)

Answer 1

Given coordinates (0,0)  and (34,-78).

$\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$We \ have\ x_1=0, x_2=34, y_1=0 \ and \ y_2=-78.$

$\mathrm{The\:distance\:between\:}\left(0,\:0\right)\mathrm{\:and\:}\left(34,\:-78\right)\mathrm{\:is\:}$

$=\sqrt{\left(34-0\right)^2+\left(-78-0\right)^2}$

$=2\sqrt{1810}$

Distance = 2(42.544) ≈ 85.09.

Therefore, distance from the origin (0,0) to the point (34,-78) is $2\sqrt{1810} \ or$ 85.09 units.