Question

If the point C(-1,2) divides internally the line segment joining A(2,5) and B in ratio 3:4, find the coordinates of B

Answer 1

Let the coordinates of B be $(\alpha ,\beta )$. It is given that AC;BC=3:4. So, the coordinates of a C are

$(\frac{3\alpha +4\times 2}{3+4},\frac{3\beta +4\times 5}{3+4})=(\frac{3\alpha +8}{7},\frac{3\beta +20}{7})$

But, the coordinates of C are (-1,2).

$\therefore \frac{3\alpha +8}{7}=-1and\frac{3\beta +20}{7}=2$

$\Rightarrow \alpha =-5and\beta =-2$

Thus, the coordinates of B are $(-5,-2)$