Distance Between Two Points

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[edit] Distance Between Two Points

A(x1,y1) and C(x2,y2) are two points on a coordinate plane as shown above. AB is parallel to the y-axis and BC is parallel to the x-axis. Hence ∆ABC = 90°.


According to Pythagoras' Theorem
AB^2 + BC^2 = AC^2 \,


Since
\, AB = y_2-y_1 and
\, BC = x_2-x_1


By substituting AB and BC into the equation
\, (y_2-y_1)^2 + (x_2-x_1)^2 = AC^2


Eliminating the square of AC by square root at both sides, we get AC =\sqrt {(x_2-x_1)^2 + (y_2-y_1)^2}


Image:note.gif Distance between 2 point, (x1,y1) and (x2,y2) can be found by the equation


Distance =\sqrt {(x_2-x_1)^2 + (y_2-y_1)^2}

[edit] Example 1: Simple question 1

Find the distance between the points:
(a) (7, 15) and (2, 5)
(b) (6,6) and (12,2)


Answer

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