# Geometry Distance Formula

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Geometry Distance Formula
Learn about Distance Formula here and understand the concept better with solved
examples provided. Students can also use the online distance formula calculator and
distance formula worksheet provided in the page.
Let's understand what is the distance formula? The length of a line segment AB, which
joins A (x1, y1) and B (x2, y2) is given by,

Know More About Circumference of Circle Formula

Distance Formula Proof
Let A (x1, y1) and B (x2, y2) be two points in the plane.
Let d = distance between the points A and B.
Draw AL and BM perpendicular to x-axis (parallel to y-axis).
Draw AC perpendicular to BM to cut BM at C.
In the figure,
OL = x1, OM = x2 [AC = LM = OM - OL = x2 - x1]
MB = y2, MC = LA = y1 [CB = MB - MC = y2 - y1]
From the right-angled DACB,
Distance Formula Examples
Below are some examples based on distance formula
Example 1:- Find the distance between the fol owing pair of points: A (1,2) and B (4,5).

Solution :-
Using the distance formula, we have
Example 2 :- Find the distance between places when the two coordinates (2, 4) and (4,
6)are given, using the distance formula.?
Solution :-
(x1, y1)= (2, 4)
(x2, y2) = (4, 6)
Example 3 :- Find the distance between places when the two coordinates (10, 15) and
(15, 20)are given, using the distance formula.?
Solution :-
(x1, y1)= (10, 15)
(x2, y2) = (15, 20)

What is Distance Formula
Learn about Distance Formula here and understand the concept better with solved
examples provided. Students can also use the online distance formula calculator and
distance formula worksheet provided in the page.
Let's understand what is the distance formula? The length of a line segment AB, which
joins A (x1, y1) and B (x2, y2) is given by,

Distance Formula Proof
Let A (x1, y1) and B (x2, y2) be two points in the plane.
Let d = distance between the points A and B.
Draw AL and BM perpendicular to x-axis (parallel to y-axis).
Draw AC perpendicular to BM to cut BM at C.
In the figure,
OL = x1, OM = x2 [AC = LM = OM - OL = x2 - x1]
MB = y2, MC = LA = y1 [CB = MB - MC = y2 - y1]
From the right-angled DACB,
Distance Formula Examples
Below are some examples based on distance formula
Example 1:- Find the distance between the fol owing pair of points: A (1,2) and B (4,5).

Solution :-
Using the distance formula, we have
Example 2 :- Find the distance between places when the two coordinates (2, 4) and (4,
6)are given, using the distance formula.?
Solution :-
(x1, y1)= (2, 4)
(x2, y2) = (4, 6)
Example 3 :- Find the distance between places when the two coordinates (10, 15) and
(15, 20)are given, using the distance formula.?
Solution :-
(x1, y1)= (10, 15)
(x2, y2) = (15, 20)

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