If A(20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.

Answer: (16, 12), (12, 14), (8, 16), (4, 18)

Let A-P-Q-R-S-B. Then P, Q, R, S divide AB in the ratios 1:4, 2:3, 3:2, 4:1.

P: \(\left(\dfrac{1(0)+4(20)}{5},\dfrac{1(20)+4(10)}{5}\right)=(16,12)\)

Q: \(\left(\dfrac{2(0)+3(20)}{5},\dfrac{2(20)+3(10)}{5}\right)=(12,14)\)

R: \(\left(\dfrac{3(0)+2(20)}{5},\dfrac{3(20)+2(10)}{5}\right)=(8,16)\)

S: \(\left(\dfrac{4(0)+1(20)}{5},\dfrac{4(20)+1(10)}{5}\right)=(4,18)\)

(Each step changes x by -4 and y by +2.)