Question

Find the co-ordinates of the points which trisects the line segment joining the point ( (0,-5) and (-3,4).

Answer 1

Let B & C trisects the line segment joining points A(0, -5) & (-3, 4).

∴ B divides AD in the ratio 1:2.

and C divides AD in the ratio 2:1.

∴ Coordinates of point B is \(\left(\frac{1 \times -3 + 2 \times 0}{1 + 2}, \frac{1 \times 4 + 2\times - 5}{1 + 2}\right)\)

or \(\left(\frac{-3}{3}, \frac{-6}3\right)\)

or \((- 1 , -2)\)

∴ Coordinates of point C is \(\left(\frac{2 \times -3 + 1 \times 0}{1 + 2}, \frac{2 \times 4 + 1\times - 5}{1 + 2}\right)\)

 or \(\left(\frac{-6}{3}, \frac{3}3\right)\)

 or \((- 2 , +1)\)

Hence, coordinates of points B(-1, -2) & C(-2, 1) which trisects the line segment joining the points which A(0, -5) & D(-3, 4).