If A(a,5) B(-1,-6) C(-4,b) are the three vertices of triangle ABC and centroid is (-1/3,2) Then find (a+b)
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2
Answer:
Let AD be the median through the vertex A of△ABC. Then, D is the mid-point of BC. So, the coorinates of D are(
2
−3−1
,
2
−2+8
)i.e.,(−2,3).
∴AD=
(5+2)
2
+(−1−3)
2
=
49+16
=
65
units
Let G be the centroid of △ABC. Then, G lies on median AD and divides it in the ratio 2:1. So, coordinates of G are
(
2+1
2×−2+1×5
,
2+1
2×3+1×−1
)=(
3
−4+5
,
3
6−1
)=(
3
1
,
3
5
)
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