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Distance Formula Questions with Detailed Solutions - Testbook

Last Updated on Jul 31, 2023
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The distance formula is a key concept in mathematics, particularly in coordinate geometry. It is used to calculate the distance between two points on a Cartesian plane. This article provides a range of distance formula questions and solutions to aid your understanding and practice of this essential skill.

The distance between two points A(x1, y1) and B(x2, y2) in a two-dimensional plane is calculated using the following formula:

Additionally, the distance between two points A(x1, y1, z1) and B(x2, y2, z2) in a three-dimensional plane can be found using the following formula:

You can delve deeper into the derivation of the distance formula by following this link.

Solving Distance Formula Questions

Let's now apply the distance formula to solve some problems.

Example 1:

Calculate the distance between the following points:

(I) (-2, 3) and (3, 4)

(II) (1, 2) and (7, -2)

(III) (2, 1, -2) and (3, 1, 8)

Solution:

(I) The distance between the points (-2, 3) and (3, 4) can be calculated as follows:

d = √[(3 - ( -2))2 + (4 - 3)2] = √[25 + 1] = √26 units.

(II) The distance between the points (1, 2) and (7, -2) can be calculated as follows:

d = √[(7 - 1)2 + (-2 - 2)2] = √[36 + 16] = √52 = 2√13 units.

(III) The distance between the points (2, 1, -2) and (3, 1, 8) can be calculated as follows:

d = √[(3 - 2)2 + (1 - 1)2 + (8 - ( -2))2] = √[1 + 0 + 100] = √101 units.

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Frequently Asked Questions

The distance between two points A(x1, y1) and B(x2, y2) in a two-dimensional plane is given by AB = sqrt((x2-x1)^2+(y2-y1)^2).

The distance between two points A(x1, y1, z1) and B(x2, y2, z2) in a three-dimensional plane is given by AB = sqrt((x2-x1)^2+(y2-y1)^2+(z2-z1)^2).

The circumcentre of a triangle is the point inside the triangle which is equidistant from all the vertices of the triangle.

The orthocentre of a triangle is the point where all the three altitudes of a triangle intersect.

The centroid of a triangle is the intersection point of all the medians of a triangle.

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