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111. Find the distance between the following pairs of points :
(2, 3), (4, 1)

Let the given points be A(2, 3) and B(4, 1).
We know that the distance between two points A(x₁, y₁) and B(x₂, y₂) is given by

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112. Find the distance between the following pairs of points :
(– 5, 7), (– 1, 3)

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113. Find the distance between the following pairs of points :
(a, b), (– a, – b)

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114.

Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.

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115.

Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear

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116.

Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

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117.

In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct.

Fig. 7.8