# Distance of a Point from the Origin

We will discuss here how to find the distance of a point from the origin.

The distance of a point A (x, y) from the origin O (0, 0) is given by OA = $$\sqrt{(x - 0)^{2} + (y - 0)^{2}}$$

i.e., OP = $$\sqrt{x^{2} + y^{2}}$$

Consider some of the following examples:

1. Find the distance of the point (6, -6) from the origin.

Solution:

Let M (6, -6) be the given point and O (0, 0) be the origin.

The distance from M to O = OM

= $$\sqrt{(6 - 0)^{2} + (-6 - 0)^{2}}$$

= $$\sqrt{(6)^{2} + (-6)^{2}}$$

= $$\sqrt{36 + 36}$$

= $$\sqrt{72}$$

= $$\sqrt{2 × 2 × 2 × 3 × 3}$$

= 6$$\sqrt{2}$$ units.

2. Find the distance between the point (-12, 5) and the origin.

Solution:

Let M (-12, 5) be the given point and O (0, 0) be the origin.

The distance from M to O = OM = $$\sqrt{(-12 - 0)^{2} + (5 - 0)^{2}}$$ = $$\sqrt{(-12)^{2} + (5)^{2}}$$

= $$\sqrt{144 + 25}$$

= $$\sqrt{169}$$

= $$\sqrt{13 × 13}$$

= 13 units.

3. Find the distance between the point (15, -8) and the origin.

Solution:

Let M (15, 8) be the given point and O (0, 0) be the origin.

The distance from M to O = OM = $$\sqrt{(15 - 0)^{2} + (-8 - 0)^{2}}$$ = $$\sqrt{(15)^{2} + (-8)^{2}}$$

= $$\sqrt{225 + 64}$$

= $$\sqrt{289}$$

= $$\sqrt{17 × 17}$$

= 17 units.

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Distance and Section Formulae