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)