Students who are looking to know the concepts of Distance and Section Formulae chapter can make use of this page. Here we provide details of all the topics with suitable examples. We will discuss how to find the distance of a point from the origin in this article. So, scroll down this page and practice the problems and try to create the questions on your own and solve them. By this, you can learn the concept and also score better marks in the exams.

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## Distance from Origin Formula

The distance of a point P(x, y) from the origin O (0, 0) is given by OP = √(x – 0)² + (y – 0)²
OP = √(x)² + (y)²

### Distance of a Point from the Origin Examples

Example 1.
Find the distance between the points (3, 4) from the origin.
Solution:
Given the point (3, 4)
Origin = (0, 0)
We know the formula to calculate the distance of a point from the origin.
The distance of a point P(x, y) from the origin O (0, 0) is given by OP = √(x – 0)² + (y – 0)²
OP = √(3 – 0)² + (4 – 0)²
OP = √(3)² + (4)²
OP = √9 + 16
OP = √25
OP = 5 units

Thus the distance between the points is 5 units.

Example 2.
Find the distance between the points (5, 5) from the origin.
Solution:
Given the point (5, 5)
Origin = (0, 0)
We know the formula to calculate the distance of a point from the origin.
The distance of a point P(x, y) from the origin O (0, 0) is given by OP = √(x – 0)² + (y – 0)²
OP = √(5 – 0)² + (5 – 0)²
OP = √(5)² + (5)²
OP = √25 + 25
OP = √50
OP = 2√5 units

Thus the distance between the points is 2√5 units.

Example 3.
Find the distance between the points (6, -3) from the origin.
Solution:
Given the point (6, -3)
Origin = (0, 0)
We know the formula to calculate the distance of a point from the origin.
The distance of a point P(x, y) from the origin O (0, 0) is given by OP = √(x – 0)² + (y – 0)²
OP = √(6 – 0)² + (-3 – 0)²
OP = √(6)² + (3)²
OP = √36 + 9
OP = √45 units

Thus the distance between the points is √45 units.

Example 4.
Find the distance between the points (1, 9) from the origin.
Solution:
Given the point (1, 9)
Origin = (0, 0)
We know the formula to calculate the distance of a point from the origin.
The distance of a point P(x, y) from the origin O (0, 0) is given by OP = √(x – 0)² + (y – 0)²
OP = √(1 – 0)² + (9 – 0)²
OP = √(1)² + (9)²
OP = √1 + 81
OP = √82 units

Thus the distance between the points is √82 units.

Example 5.
Find the distance between the points (-5, -4) from the origin.
Solution:
Given the point (-5, -4)
Origin = (0, 0)
We know the formula to calculate the distance of a point from the origin.
The distance of a point P(x, y) from the origin O (0, 0) is given by OP = √(x – 0)² + (y – 0)²
OP = √(-5 – 0)² + (-4 – 0)²
OP = √(5)² + (4)²
OP = √25 + 16
OP = √41 units

Thus the distance between the points is √41 units.

### FAQs on Distance of a Point from the Origin

1. What is the distance of a number from the origin?

Absolute Value is the distance of a number from the origin.

2. What is the distance of the point (-2 4) from the origin?

Given the point (-2, 4)
Origin = (0, 0)
We know the formula to calculate the distance of a point from the origin.
The distance of a point P(x, y) from the origin O (0, 0) is given by OP = √(x – 0)² + (y – 0)²
OP = √(-2 – 0)² + (4 – 0)²
OP = √(2)² + (4)²
OP = √4 + 16
OP = √20 units

3. What is the formula to find the distance of a point from the origin?

The distance of a point P(x, y) from the origin O (0, 0) is given by OP = √(x – 0)² + (y – 0)²
OP = √(x)² + (y)²