Question

P(2,-1) and Q(4,0) divide $\overline{AB}$ from A' s side in the ratios 2:1 and -2:1 respectively. find the co-ordinates of A and B.

Answer 1

R.E.F image

Let the co-ordinate of A be $(x_1,y_1)$ and

B be $(x_2,y_2)$

So, using the given co-ordinates of form equation

in x and y :

(i) $2=\frac{x_1+2x_2}{3}\Rightarrow 6=x_1+2x_2$

(ii) $4=\frac{x_1-2x_2}{1}\Rightarrow -4=x_1-2x_2$

$\ast$ Solving the two equations, we get $x_1=1$ and $x_2=\frac{-5}{2}$

Similarly,

(iii) $-1=\frac{y_1+2y_2}{3}\Rightarrow -3=y_1+2y_2$

(iv) $0=\frac{y_1+\left(2y_2\right)}{-1}\Rightarrow 0=y_1-2y_2$

Solving, these two equations, we get $y_1=\frac{-3}{2}$ and $y_2=\frac{-3}{4}$