# 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.

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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