Points P, Q, R and S divide the line segment joining the points A(1, 2) and B(6, 7) in five equal parts. Find the coordinates of the points P, Q and R.
P divides the segment AB in ratio 1:4
Q divides the segment AB in ratio 2:3
R divides the segment AB in ratio 3:2
For coordinates of P
X = (m1x2 + m2x1)/ m1 + m2
= (1 × 6 + 4 × 1)/1 + 4
= (6 + 4) /5
= 10/5 = 2
Y = (m1y2 + m2y1)/ m1 + m2
= (1x 7 + 4 × 2)/5
= (7 + 8)/5
= 15 / 5 = 3
= (2, 3)
For coordinates of Q
X = (m1x2 + m2x1)/ m1 + m2
= (2x 6 + 3x 1)/5
= (12 + 3) /5
= 15/5 = 3
Y = (m1y2 + m2y1)/ m1 + m2
= (2 × 7 + 3 × 2)/ 5
= (14 + 6)/5
= 20 / 5 = 4
= (3,4)
For coordinates of R
X = (m1x2 + m2x1)/ m1 + m2
= (3 × 6 + 2 × 1)/5
= (18 + 2) /5
= 20/5 = 4
Y = (m1y2 + m2y1)/ m1 + m2
= (3 × 7 + 2 × 2)/ 5
= (21 + 4)/5
= 25 / 5 = 5
= (4,5)
Hence
P(2, 3), Q(3, 4), R(4, 5)