Question

If $A(-2,5)$ and $B(3,2)$ are the points on a straight line. If $AB$ is extended to ${}^{\prime }{C}^{\prime }$ such that $AC=2BC$, then the co-ordinates of ${}^{\prime }{C}^{\prime }$ are ____

• A. $\left(\frac{1}{2},\frac{3}{2}\right)$
• B. $\left(\frac{7}{2},\frac{1}{2}\right)$
• C. $(8,-1)$
• D. $(-1,8)$

Answer 1

The correct option is C $(8,-1)$

Given points are $A(-2,5)$ and $B(3,2)$

$\frac{AC}{BC}=\frac{2}{1}$ , $C$ divides line segment $AB$ externally.

If $A(x_1,y_1)$ and $B(x_2,y_2)$ be two end points of a line segment, then the coordinates of the point $P(x,y)$ that divides the line segment externally in the ratio $m:n$ is $(\frac{m{x}_2-n{x}_1}{m-n},\frac{m{y}_2-n{y}_1}{m-n})$.

Thus, the coordinates of $C$ are $(\frac{2\left(3\right)-1(-2)}{2-1},\frac{2\left(2\right)-1\left(5\right)}{2-1})$.

$=(\frac{6+2}{1},\frac{4-5}{1})$

$=(8,-1)$