Q. 24.8( 5 Votes )

# Prove that by joining the point (2, 1), (3, 4), (– 3, 6) we get a right triangle.

Answer :

**Let** A = (2,1)

B = (3,4)

C = (– 3,6)

Length of Side

AB = distance between point A and B =

Here x_{2} = 3,y_{2} = 4,x_{1} = 2,y_{1} = 1

∴ AB =

∴ AB =

∴ AB =

**∴** **AB = √10 units**

BC = distance between point B and C =

Here x_{2} = – 3,y_{2} = 6,x_{1} = 3,y_{1} = 4

∴ BC =

∴ BC =

∴ BC =

**∴** **BC = √40units**

CA = distance between point C and A =

Here x_{2} = 2,y_{2} = 1,x_{1} = – 3,y_{1} = 6

∴ CA =

∴ CA =

∴ CA =

**∴** **CA = √50 units**

Here CA is the largest side.

For ΔABC to be right angled triangle

Here,

And

50 = 50

⇒

∴ the given triangle is a right – angled triangle.

**Hence Proved.**

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Prove that by joining the point (2, 1), (3, 4), (– 3, 6) we get a right triangle.

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