Question

find the cordinates of points of trisection of line segment joining the points a (1,-2)and b(-3,-4)​

Answer 1

$\underline\mathtt{Question:}$

Find the cordinates of points of trisection of line segment joining the points A(1,-2)and B(-3,-4)

$\underline\mathtt{Answer:}$

Let the points of trisection be P (x, y) and Q (r, s)

P (x, y) divides AB in the ratio 1 : 2, using section formula

$P (x, y) = (\frac{m x_{2} + n x_{1} }{m + n} , \frac{m y_{2} + n y_{1} }{m + n} )$

$= (\frac{1( - 3) + 2(1)}{1 + 2} , \frac{1( - 4) + 2( - 2)}{1 + 2} )$

$= ( \frac{ - 1}{3} , \frac{ - 8}{3} )$

Now the point P is midpoint of AQ, we can use the midpoint formula and find Q (refer to the image)

$Q(r, s) = ( \frac{ - 5}{3} , \frac{ - 10}{3} )$

Therefore the points of trisection of AB are (-1/3, -8/3) and (-5/3, -10/3)

Have a good evening!