Theorem 1 : If the coordinates of two points are (x_{1},
y_{1}) and (x_{2}, y_{2}), then the distance
d between them is given by the formula :
Example 1
Using the distance formula determine the distance between the points with coordinates ( 4, 2 ) and (6, 3 ).
Solution :
Let (4, 2) be (x_{1}, y_{1}) and
(6, 3) be (x_{2}, y_{2}). Then according to the distance formula,
Example 2
A triangle has vertices A (2,2), B (5,2) and C (5,6). Show that the triangle is a right angled triangle.
Solution :
By the distance formula
\
d(AC) = 5, d (AB) = 3, and d (BC) = 4
According to Pythagorean if the sum of the square of two sides are equal to the square of the third side then the triangle is a right angled triangle.
Therefore, the triangle is right angled triangle.
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