Q. 64.3( 20 Votes )

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.

Answer :

Given A (3, 3)


B (8, -2)


C (-2, -2)


are the vertices of a triangle.


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


Using the above distance formula,


AB





BC




= 10


CA





Now, (AB)2 + (CA)2


and (AB)2


We find that (AB)2 + (CA)2 = (BC)2 and AB = CA.


Hence proved that the three points A(3, 3), B(8, –2) and C(–2, –2) are the vertices of a right-angled isosceles triangle.


Length of hypotenuse BC = 10 units.


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RELATED QUESTIONS :

Let us calculate the distances between the two points given below:

(i) (5, 7) and (8, 3)


(ii) (7, 0) and (2, –12)


(iii) and (0, –2)


(iv) (3, 6) and (–2, –6)


(v) (1, –3) and (8, 3)


(vi) (5, 7) and (8, 3)

West Bengal Mathematics