Show that the points A(7, 10), B(-2, 5) and c(3, -4) are the vertices of an isosceles right triangle
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Given points are A(7,10),B(−2,5) and C(3,−4)
AB
2
=(x
2
−x
1
)
2
+(y
2
−y
1
)
2
=(−2−7)
2
+(5−10)
2
=(−9)
2
+(−5)
2
=81+25=106
BC
2
=(3+2)
2
+(−4−5)
2
=(5)
2
+(−9)
2
=25+81=106
CA
2
=(7−3)
2
+(10+4)
2
=(4)
2
+(14)
2
=16+196=212
AB
2
+BC
2
=106
⇒AB=BC
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
+BC
2
=106+106=212=CA
2
Hence given points are vertices of an isosceles right triangle.
Step-by-step explanation:
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