Question

Find yhe coordinates of teo points which divide the line segment joining (1.,5) (-5,-7) inthi three equal parts

Answer 1

Given that the line is divided internally into three parts.

∴ Ratio of the first point dividing the line = 1:2

∴ Ratio of the second point dividing the line = 2:1

By using section formula,

first point = (mx₂+nx₁/m+n) , (my₂+ny₁/ m+n)

                = (1×-5 + 2×1 / 1+2) , (1×-7 + 1×5/ 1+2)

                = ( -5 + 2/3) , (-7 + 5/3)

                = (-3/3) , (-2/3)

⇒ coordinates = (-1 , -2/3)

Second point:

using section formula = (mx₂+nx₁/m+n) , (my₂+ny₁/m+n)

                                    = (2×-5+1×1/2+1)  , (2×-7+1×5/2+1)

                                    = (-10+1/3) , (-14+5/3)

                                    = (-9/3) , (-9/3)

                                    ⇒ (-3,-3)

∴Two coordinates =  (-1, -2/3) & (-3,-3)