Find the coordinates of the points which divide the line segment joining A(-2,2) and B(2,8) into four equal parts.

Let P, Q, R be the points which divide the line into 4 equal parts.
Then the ratio of AP and PB = m1:m2 = 1:3
Here A(x1, y1) = A(-2, 2), B(x2, y2) = B(2, 8)
∴Coordinates of P = (m1x2 + m2x1 / m1 + m2, m1y2 + m2y1 / m1 + m2)
→ (1 × 2 - 2 × 3 / 1 + 3, 1 × 8 + 3 × 2 / 1 + 3)
→ (2 - 6 / 4, 8 + 6 / 4) = (-1, 7/2)
The ratio of AQ and QB = m1:m2 = 2:2
Here A(x1, y1) = A(-2, 2), B(x2, y2) = B(2, 8)
∴Coordinates of Q = (m1x2 + m2x1 / m1 + m2, m1y2 + m2y1 / m1 + m2)
→ (2 × 2 + 2 × -2 / 2 + 2, 2 × 8 + 2 × 2 / 2 + 2)
→ (4 - 4 / 4, 16 + 4 / 4) = (0, 5)
Then the ratio of AR and RB = m1:m2 = 3:1
Here A(x1, y1) = A(-2, 2), B(x2, y2) = B(2, 8)
∴Coordinates of R = (m1x2 + m2x1 / m1 + m2, m1y2 + m2y1 / m1 + m2)
→ (3 × 2 + 1 × -2 / 3 + 1, 3 × 8 + 1 × 2 / 3 + 1)
→ (6 - 2 / 4, 24 + 2 / 4) = (1, 13/2)
∴Coordinates are P(-1, 7/2), (0, 5), (1, 13/2)