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 x2 = 3,y2 = 4,x1 = 2,y1 = 1
∴ AB = 
∴ AB = 
∴ AB = 
∴ AB = √10 units
BC = distance between point B and C = 
Here x2 = – 3,y2 = 6,x1 = 3,y1 = 4
∴ BC = 
∴ BC = 
∴ BC = 
∴ BC = √40units
CA = distance between point C and A = 
Here x2 = 2,y2 = 1,x1 = – 3,y1 = 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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