Answer :

P divides the segment AB in ratio 1:3


Q divides the segment AB in ratio 2:2


R divides the segment AB in ratio 3:1


For coordinates of P


X = (m1x2 + m2x1)/ m1 + m2


= (1 × 5 + 3 × 1)/1 + 3


= (5 + 3) /4


= 8/4 = 2


Y = (m1y2 + m2y1)/ m1 + m2


= (1× (– 2) + 3 × 6)/4


= (– 2 + 18)/5


= 16 / 4 = 4


= (2, 4)


For coordinates of Q


X = (m1x2 + m2x1)/ m1 + m2


= (2x 5 + 2x 1)/4


= (10 + 2) /4


= 12/4 = 3


Y = (m1y2 + m2y1)/ m1 + m2


= (2 × (– 2) + 2 × 6)/ 4


= (– 4 + 12)/4


= 8 / 4 = 2


= (3,2)


For coordinates of R


X = (m1x2 + m2x1)/ m1 + m2


= (3x 5 + 1x 1)/4


= (15 + 1) /4


= 16/4 = 4


Y = (m1y2 + m2y1)/ m1 + m2


= (3 × (– 2) + 1 × 6)/ 4


= (– 6 + 6)/4


= 0/ 4 = 0


= (4,0)


the coordinates are P(2, 4), Q(3, 2), R (4, 0)


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