A(-1,3), B(5,2) and C(5,-2) arethe vertices of a triangle. (i)Find the coordinates of thecentroid G of the triangle(ii)Find the equation of the linethrough G and parallel to AC *
A(-1,3), B(5,2) and C(5,-2) arethe vertices of a triangle. (i)Find the coordinates of thecentroid G of the triangle(ii)Find the equation of the linethrough G and parallel to AC *
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Step-by-step explanation:
ANSWER
Given, A(−1,3),B(4,2),C(3,−2)
(i) Co-ordinates of centroid G is
G(x,y)=(
2
(x
1
+x
2
+x
3
)
,
2
(y
1
+y
2
+y
3
)
)
=(
3
(−1+4+3)
,
3
(3+2−2)
)
=(
3
6
,
3
3
)=(2,1)
Hence, the co-ordinates of the centroid G of the triangle is (2,1)
(ii) Slope of AC=
(x
2
−x
1
)
(y
2
−y
1
)
=
(3−(−1))
(−2−3)
=
4
−5
So, the slope of the line parallel to AC is also
4
−5
Now, the equation of line through G is
y−1=(
4
−5
)(x−2)
4y−4=−5x+10
5x+4y=14
Thus, the required line equation 5x+4y=14.
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