Find the coordinates of the point C which lies on the line AB produced such that AC = 2BC , where coordinates of…

CBSE Class 10 Maths PYQ · Coordinate Geometry · Application · 2 Marks · March 2025 · Standard

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1162 Marks · March 2025 · Standard

Find the coordinates of the point C which lies on the line AB produced such that $AC = 2BC$, where coordinates of points A and B are $(-1, 7)$ and $(4, -3)$ respectively.

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Let coordinates of point C be $(x, y)$. $AC = 2BC \implies B$ is mid-point of $AC$. $\frac{-1+x}{2} = 4 \implies x = 9$. $\frac{7+y}{2} = -3 \implies y = -13$. $\therefore$ Coordinates of C are $(9, -13)$.