Question

Segment AB is divided into four equal parts by points P, Q and R such that A – P – Q – R – B. If P(12, 9) and R(0, 11), then find the coordinates of points A, Q and B

Answer 1

Answer:

A(18, 8)

Q(6, 10)

B(-6, 12)

Step-by-step explanation:

Let co-ordinate of A = (x, y)

co-ordinate of B = (x', y')

P(12, 9)

R(0, 11)

Q is the midpoint of PR

So, Q = (12 + 0 / 2, 9 + 11 / 2)

Q = (6, 10)

P divides AQ in ratio 1:1

12 = 6 + x / 1 + 1 and 9 = y + 10/ 1 + 1

12 = 6 + x / 2 and 9 = y + 10 / 2

12 × 2 = 6 + x and 9 × 2 = y + 10

24 - 6 = x and 18 - 10 = y

x = 18 and y = 8

So, A(18, 8)

R divides QB in ratio 1:1

0 = x' + 6 / 1 + 1 and 11 = 10 + y' / 1 + 1

0 = x' + 6 / 2 and 11 = 10 + y' / 2

0 × 2 = x' + 6 and 11 × 2 = 10 + y'

0 - 6 = x' and 22 - 10 = y'

x' = -6 and y' = 12

So, B(-6, 12).