# The coordinate of the point A

Thecoordinate of the point A

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(a) Mid-pt of BC is (2.5, 6), therefore, the equation of the median passes through A is :

(y - 3)/(x - 1) = (6 - 3)/(2.5 - 1)

==> y - 3 = 2x - 2

==> 2x - y + 1 = 0

Mid-pt of AC is (4, 5.5), therefore, the equation of the median passes through B is :

(y - 4)/(x + 2) = (5.5 - 4)/(4 + 2)

==> 4y - 16 = x + 2

==> x - 4y + 18 = 0

(b) The intersection point of the medians is to solve these two equations :

2x - y + 1 = 0 ⋯⋯⋯ (i)

x - 4y + 18 = 0 ⋯⋯ (ii)

(I) - 2*(ii), gets,

7y - 35 = 0

==> y = 5

Sub y = 5 into (I), gets x = 2

As the centroid is the intersection point of the medians,

Therefore, the centroid is (2, 5).

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