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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 = β(xβ0)2+(yβ0)2
i.e., OP = βx2+y2
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
= β(6β0)2+(β6β0)2
= β(6)2+(β6)2
= β36+36
= β72
= β2Γ2Γ2Γ3Γ3
= 6β2 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 = β(β12β0)2+(5β0)2 = β(β12)2+(5)2
= β144+25
= β169
= β13Γ13
= 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 = β(15β0)2+(β8β0)2 = β(15)2+(β8)2
= β225+64
= β289
= β17Γ17
= 17 units.
β Distance and Section Formulae
10th Grade Math
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