Question

the points of trisection of the line segment joiming (4,-1) and (-2,-3)​

Answer 1

Answer:

Using the section formula, if a point (x,y) divides the line joining the points (x1 ,y1 ) and (x2,y2 ) in the ratio m:n, then

$(x \:, y) = (\frac{mx2 + nx1}{m + n} , \frac{my2 + ny1}{m + n} )$

Let P and Q be the points of trisection of line joining the points A(4,1) & B(-2,-3).

Then, AP = PQ = QB

Now, P divides AB in the ratio 1:2 and Q divides AB in the ratio 2:1.

Therefore,

$Coordinates \: of \: P =  (\frac{ - 7 + 4}{3} , \frac{4 - 4}{3} ) \\ ( - 1,0)$

$Coordinates \: of \: Q = ( \frac{ - 14 + 2}{3} , \frac{8 - 2}{3} ) \\ ( - 4,2)$

$Hence, \: the \: two \: points \: of \: trisection \: are \:  P(−1,0) \:  and  \: (−4,2).</p><p>$