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.

● Distance and Section Formulae

• Distance Formula
• Distance Properties in some Geometrical Figures
• Conditions of Collinearity of Three Points
• Problems on Distance Formula
• Distance of a Point from the Origin
• Distance Formula in Geometry
• Section Formula
• Midpoint Formula
• Centroid of a Triangle
• Worksheet on Distance Formula
• Worksheet on Collinearity of Three Points
• Worksheet on Finding the Centroid of a Triangle
• Worksheet on Section Formula

10th Grade Math

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