The co-ordinates of the centroid of a triangle ABC are (1, -4). What are the co-ordinates of vertex C if co-ordinates of A and B are (3, -4) and (0, 5) respectively?
(0, -13)
For centroid \(G(\bar x,\bar y)\) of triangle with vertices \((x_i,y_i)\):
\[\bar x = \dfrac{x_1+x_2+x_3}{3},\quad \bar y = \dfrac{y_1+y_2+y_3}{3}\]
x-coordinate: \(1 = \dfrac{3+0+x_3}{3} \Rightarrow x_3 = 0\).
y-coordinate: \(-4 = \dfrac{-4+5+y_3}{3} \Rightarrow y_3 = -13\).
Hence C = (0, -13).
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In which quadrant both abscissa and ordinate are negative?
Find the slope of the line joining the points (3, -4) and (5, 2).
Find the value of K for which equation x – Ky = 2, 3x + 2y = 5 has unique solution.
