Q7 of 20 Page 52

Let us show by calculation that the points (2, 1), (0, 0), (–1, 2) and (1, 3) are the angular points of a square.

We have A → (2, 1)


B → (0, 0)


C → (-1, 2)


D → (1, 3)


We know that distance between two points (x1, y1) and (x2, y2) is given by .


Using the above distance formula,


AB





BC





CD





DA





Now, consider the diagonals, AC and BD.


AC





BD





We find that AB = BC = CD = DA with equal diagonals (AC = BD)


⇒ ABCD is a square.


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5

Let us prove that in both of the following cases, the three points are the vertices of an isosceles triangle:

(i) (1, 4), (4, 1) and (8, 8)


(ii) (–2, –2), (2, 2) and (4, –4)

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Let us prove that the three points A(3, 3), B(8, –2) and C(–2, –2) are the vertices of a right-angled isosceles triangle. Let us calculate the length of the hypotenuse of ΔABC.

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