Question

Find the points of trisection of the segment joining A ( -3, 7) and B (3, -2). 

Answer 1

Let P (x, y) and Q (a, b) be the pcint of trisection of the line segment AB .

AP : PB = 1 : 2 

Coordinates of P are 

x = `(1 xx 3 + 2 xx -3)/(1 + 2) = -1`

y = `(1 xx -2 + 2 xx 7)/(1 + 2) = 4`

P (-1, 4) 

AQ : QB = 2 : 1

coordinates of Q are, 

a = `(2 xx 3 = 1 xx -3)/(2 + 1) = 1`

b = `(2 xx - 2 + 1 xx 7)/(2 + 1) = 1`

Q (1 , 1)

∴ The points of trisection ae (- 1, 4)and (1, 1).