If A and B are the points (-3, 4) and (2, 1), | vedclass

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Question

(C) Given $AC = 2 BC$,we have $\frac{AC}{BC} = \frac{2}{1}$.Since $C$ lies on $AB$ produced,$C$ divides the line segment $AB$ externally in the ratio

Vedclass · Accepted Answer

$(7, -2)$

Vedclass · Answer

(C) Given $AC = 2 BC$,we have $\frac{AC}{BC} = \frac{2}{1}$.Since $C$ lies on $AB$ produced,$C$ divides the line segment $AB$ externally in the ratio $m:n = 2:1$.The coordinates of a point dividing the segment joining $(x_1, y_1)$ and $(x_2, y_2)$ externally in the ratio $m:n$ are given by $\left(\frac{mx_2 - nx_1}{m-n}, \frac{my_2 - ny_1}{m-n}\right)$.Substituting $(x_1, y_1) = (-3, 4)$,$(x_2, y_2) = (2, 1)$,$m = 2$,and $n = 1$:$x = \frac{2(2) - 1(-3)}{2-1} = \frac{4 + 3}{1} = 7$$y = \frac{2(1) - 1(4)}{2-1} = \frac{2 - 4}{1} = -2$Thus,the coordinates of $C$ are $(7, -2)$.

If $A$ and $B$ are the points $(-3, 4)$ and $(2, 1)$,then the coordinates of the point $C$ on $AB$ produced such that $AC = 2 BC$ are:

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