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 (x_{1}, y_{1}) and (x_{2}, y_{2}) 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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