Name the type of triangle formed by the points A (2,-2), B (-2, 1), C (5, 2). Justify your answer.
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Answer:
The three vertices of the triangle are A(−5,6),B(−4,−2) and (7,5).
By distance formula, AB =
[(x
2
−x
1
)
2
+(y
2
−y
1
)
2
]
AB =
[(−4−(−5))
2
+(4−(−2−6))
2
]
AB =
[(1)
2
+(−8)
2
]
AB =
[1+64]
AB =
65
By distance formula, AC =
[(x
2
−x
1
)
2
+(y
2
−y
1
)
2
]
AC =
[(7−(−5))
2
+(5−6)
2
]
AC =
[(12)
2
+(−1)
2
]
AC =
144+1]
AC =
145
By distance formula, BC =
[(x
2
−x
1
)
2
+(y
2
−y
1
)
2
]
BC =
[(7−(−4))
2
+(5−(−2))
2
]
BC =
[(11)
2
+(7)
2
]
BC =
[121+49]
BC =
170
Length of all sides of the triangle are different.
So ABC is a scalene triangle.
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