Find the coordinates of the points of trisection of the line segment joining the points A(7, –2) and B(1, –5).
Find the coordinates of the points of trisection of the line segment joining the points A(7, –2) and B(1, –5).
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;
$\mathrm{P}(x, y)=\left(\frac{1 \times 1+2 \times 7}{3}, \frac{1 \times-5+2 \times-2}{3}\right)$
$\mathrm{P}(x, y)=\left(\frac{15}{3}, \frac{-9}{3}\right)=(5,-3)$
Similarly, coordinates of Q are;
$\mathrm{Q}(a, b)=\left(\frac{2 \times 1+1 \times 7}{3}, \frac{2 \times-5+1 \times-2}{3}\right)$
$\mathrm{Q}(a, b)=\left(\frac{9}{3}, \frac{-12}{3}\right)=(3,-4)$
Therefore, coordinates of points P and Q are (5,
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.