The line segment joining the points A(3, – 4) and B(1, 2) is trisected at the points P(p, – 2) and Q(5/3, q). Find the values of p and q.

Question

Philoid · Accepted Answer

P divides the segment AB in ratio 1:2

Q divides the segment AB in ratio 2:1

For coordinates of P

X = (m₁x₂ + m₂x₁)/ m₁ + m₂

= (1 × 1 + 2 × 3)/1 + 2

= (1 + 6) /3

= 7/3 = p

Y = (m₁y₂ + m₂y₁)/ m₁ + m₂

= (1x2 + 2 × (– 4))/3

= (2 – 8)/3

= – 6/ 3 = – 2

For coordinates of Q

X = (m₁x₂ + m₂x₁)/ m₁ + m₂

= (2x 1 + 1x 3)/3

= (2 + 3) /3

= 5/3

Y = (m₁y₂ + m₂y₁)/ m₁ + m₂

= (2 × 2 + 1 × (– 4))/3

= (4 – 4)/3

= 0/ 3

= 0 = q

p = 7/3 , q = 0