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. [3 MARKS]

Answer 1

Formula: 1 Mark
Concept:1 Mark
Answer: 1 Mark

Let the coordinates of B be $(\alpha ,\beta )$.

It is given that AC:BC = 3:4.

So, the coordinates of C are:

$C(x,y)=\left(\frac{m{x}_2+n{x}_1}{m+n}\right),\left(\frac{m{y}_2+n{y}_1}{m+n}\right)$

$\Rightarrow C(-1,2)=\frac{3\alpha +4\times 2}{3+4},\frac{3\beta +4\times 5}{3+4}$

$\Rightarrow C(-1,2)=\frac{3\alpha +8}{7},\frac{3\beta +20}{7}$

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

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

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