Question

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

Answer 1

Let the coordinates of B be $\left(x_1,y_1\right)$.
Then, P divides the line joining A(2, 5) and B$\left(x_1,y_1\right)$ in the ratio 3 : 4.
So, by section formula, the coordinates of P are
$$\begin{gathered} P\left(\frac{3x_1+8}{3+4},\frac{3y_1+20}{3+4}\right) \\ i.e.P\left(\frac{3x_1+8}{7},\frac{3y_1+20}{7}\right) \end{gathered}$$

But, the coordinates of P are (−1, 2).

$\frac{3x_1+8}{7}=-1\text{and}\frac{3y_1+20}{7}=2$

$\Rightarrow 3x$₁+8=−7 and 3y₁+20=14

$$\begin{gathered} \Rightarrow x_1=-15\text{and}3y_1=-6 \\ \Rightarrow x_1=-5\text{and}{y}_1=-2 \end{gathered}$$

Hence, the coordinates of B are (−5, −2).