Question

Find the coordinates of the points of trisection of the line segment joining the points A(7, –2) and B(1, –5). [CBSE 2017]

Answer 1

Consider the figure.
Here points P and Q trisect AB.
Therefore, P divides AB into 1 : 2 and Q divides AB into 2 : 1.
Using section formula, coordinates of P are;
$$\begin{gathered} \mathrm{P}(x,y)=\left(\frac{1\times 1+2\times 7}{3},\frac{1\times -5+2\times -2}{3}\right) \\ \mathrm{P}(x,y)=\left(\frac{15}{3},\frac{-9}{3}\right)=\left(5,-3\right) \end{gathered}$$
Similarly, coordinates of Q are;
$$\begin{gathered} \mathrm{Q}(a,b)=\left(\frac{2\times 1+1\times 7}{3},\frac{2\times -5+1\times -2}{3}\right) \\ \mathrm{Q}(a,b)=\left(\frac{9}{3},\frac{-12}{3}\right)=\left(3,-4\right) \end{gathered}$$
Therefore, coordinates of points P and Q are (5, $-$3) and (3, $-$4) respectively.