The vertices of a triangle are A(a, 0), B(0, b) and C(a, b)
a b b
The centroid of AABC is
a)
2'2
8.
(2a
9. The mid point of AB is
b
)
129
3
10.
The mid point of BC is
c) a,
a
11. The mid point of AC is
d)
2.
74
Var
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Answer:
The given vertices represent a right angled triangle with right angle at C(a,b) and the hypotenuse AB, as AB
2
=AC
2
+BC
2
So that orthocentre of the triangle is at C(a,b).
Circumcentre of the triangle is the middle point of the hypotenuse AB i.e. (a/2,b/2)
And centroid of the triangle is
(
3
a+a+0
,
3
0+b+b
)=(
3
2a
,
3
2b
)
Let P(x,y) be the foot of the altitude from C.
Then P lies on AB whose equation is
a
x
+
b
y
=1 ( 1 )
Also CP is perpendicular to AB and its equation
⇒y−b=(a/b)(x−a) ( 2 )
Solving (1) & (2) we get
x=
a
2
+b
2
a
3
,y=
a
2
+b
2
b
3
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