Show that the points (−3, −4), (2, 6) and (−6, 10) are vertices of a triangle. Hence, prove that
the triangle is a right-angled triangle. Find area of the triangle.
Answers
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♣ ANSWER:-
Using the distance formula d=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
, we get
AB
2
=(2+3)
2
+(6+4)
2
=5
2
+10
2
=25+100=125
BC
2
=(−6,−2)
2
+(10−6)
2
=(−8)
2
+4
2
=64+16=80
CA
2
=(−6+3)
2
+(10+4)
2
=(−3)
2
+(14)
2
=9+196=205
i.e., AB
2
+BC
2
=125+80=205=CA
2
Hence ABC is a right angled triangle since the square of one side is equal to sum of the squares of the other two sides.
hopefully it helps
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