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.
10th Grade Math
From Distance of a Point from the Origin to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.