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# A (– 1, 3) , B (4, 2) and C (3, – 2) are the vertices of a triangle. (i) Find the coordinates of the centroid G of the triangle. (ii) Find the equation of the line through G and parallel to AC. Solution:

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M.L Aggarwal book Important Question of class 10 chapter Based on Equation of a Straight Line for ICSE BOARD.
Vertices of a triangle is given.
You have to find the coordinates of the centroid of the triangle and the equation of the line through G and parallel to AC.
This is the Question Number 28, Exercise 12.2 of M.L Aggarwal.

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1. Given, A (– 1, 3), B (4, 2), C (3, – 2)

(i) Co-ordinates of centroid G is

G (x, y) = ((x1 + x2 + x3)/2, (y1+ y2 + y3)/2)

= ((-1 + 4 + 3)/3, (3 + 2 – 2)/3)

= (6/3, 3/3) = (2, 1)

Hence, the co-ordinates of the centroid G of the triangle is (2, 1)

(ii) Slope of AC = (y2 – y1)/ (x2 – x1) = (-2 – 3)/ (3 – (-1)) = -5/4

So, the slope of the line parallel to AC is also -5/4

Now, the equation of line through G is

y – 1 = (-5/4) (x – 2)

4y – 4 = -5x + 10

5x + 4y = 14

Thus, the required line equation is 5x + 4y = 14.

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