Question

The quadrant in which the point dividing the line segment joining the points (7, –6) and (3, 4) internally in the ratio 1 : 2 is _________.

Answer 1

Let P(x, y) be the point dividing the line segment joining the points (7, –6) and (3, 4) internally in the ratio 1 : 2

Section formula: if the point (x, y) divides the line segment joining the points (x₁, y₁) and (x₂, y₂) internally in the ratio m : n, then the coordinates (x, y) = $\left(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n}\right)$

Therefore, using section formula, the coordinates of P are:

$$\begin{gathered} \left(x,y\right)=\left(\frac{1\left(3\right)+2\left(7\right)}{1+2},\frac{1\left(4\right)+2\left(-6\right)}{1+2}\right) \\ =\left(\frac{3+14}{3},\frac{4-12}{3}\right) \\ =\left(\frac{17}{3},\frac{-8}{3}\right) \\ =\left(\frac{17}{3},-\frac{8}{3}\right) \end{gathered}$$

Hence, the quadrant in which the point dividing the line segment joining the points (7, –6) and (3, 4) internally in the ratio 1 : 2 is IV quadrant.