A triangle has vertices A (0,-5), B (-2, 1) and C (10,5). Show that it is a right-angled triangle.
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1
Answer:
Hmm
Step-by-step explanation:
Let A(x
1
,y
1
)=(3,2),B(x
2
,y
2
)=(2,−3) and C(x
3
,y
3
)=(0,0)
∴ Distance between two points =
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
AB=
(2−3)
2
+(−3−2)
2
=
1+25
=
26
units
BC=
(0−2)
2
+(0+3)
2
=
4+9
=
13
units
CA=
(0−3)
2
+(0−2)
2
=
9+4
=
13
units
(
13
)
2
+(
13
)
2
=(
26
)
2
∴BC
2
+CA
2
=AB
2
Hence the given points form a right-angled triangle.
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