Show that the mid point of line joining points (-5,12) and (-1,-12) is a point of trisection of the line joining the points (-8,-5) and (7,10).

Answer 1

midpoint of (-5,12) and (-1,-12)
= ( (-5-1)/2 , (12-12)/2 ))
= (-3, 0)

I will use vectors to find the points of trisection
i.e. in the ratio of 1:2
one point = (1/3)(7,10) + (2/3)(-8,-5)
= (7/3, 10/3) + (-16/3 , -10/3)
= (-9/3 , 0)
= (-3,0)

which is the midpoint of above

other point = (1/3)(-5,12) + (1/3)(-1,-12)
= (-5/3 , 4) + (-1/3 , -4)
= (-2 , 0)

Answer 2

This answer helped me