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Question
A(-1, 3), B(4, 2) and C(3, -2) are the vertices of a triangle.
1) Find the coordinates of the centroid G of the triangle
2) Find the equation of the line through G and parallel to AC
Solution
Given vertices: A( 1, 3), B(4, 2) and C(3, 2)
1) Coordinates of the centroid G of ΔABC are given by
`G = ((-1+4+3)/3 , (3+2-2)/3) = (6/3, 3/3) = (2,1)`
2) Since the line through G is parallel to AC the slope of the lines are the same
`=> m = (y_2-y_1)/(x_2-x_1) = (-2-3)/(3-(-1)) = (-5)/4`
So, equation of the line passing throughG(2, 1) and with slopew `(-5)/4` is given by
`y - y_1 = m(x-x_1)`
`=> y - 1 = (-5)/4 (x - 2)`
`=> 4y - 4 = -5x + 10`
`=> 5x + 4y = 14` is the reuired equation.
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