Question : 3
Prove that the pointsA(3,0). B) and 6.1 are the vertices of an isosceles right triangle
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and C(−1,3) are the vertices of an isosceles right triangle.
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Given points are A(3,0),B(6,4) and C(−1,3)
AB
2
=(x
2
−x
1
)
2
+(y
2
−y
1
)
2
=(6−3)
2
+(4−0)
2
=3
2
+4
2
=9+16=25
BC
2
=(−1−6)
2
+(3−4)
2
=(−7)
2
+(−1)
2
=49+1=50
CA
2
=(3+1)
2
+(0−3)
2
=4
2
+3
2
=16+9=25
AB
2
=CA
2
=25
AB=CA
From above, two of the sides are of equal length, so triangle ABC is an isosceles triangle.
Check for: Isosceles right triangle
Sum of square of two sides = Square of third side
AB
2
+AC
2
=25+25=50=CB
2
Hence given points are vertices of an isosceles right triangle.
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