Question

Find the coordinates of the points of trisection of the line segment joining the points A(7, –2) and B(1, –5).

Answer 1

Given: A(7, –2), B(1, –5)

Step-wise calculation:

1. Vector from A to B:

B – A = (1 – 7, –5 – (–2))

= (–6, –3)

2. First trisection point (one-third from A):

`A + (1/3)(B - A) = (7, -2) + (1/3)(-6, -3)`

= (7 – 2, –2 – 1)

= (5, –3)

3. Second trisection point (two-thirds from A):

`A + (2/3)(B - A) = (7, -2) + (2/3)(-6, -3)`

= (7 – 4, –2 – 2)

= (3, –4)

The points of trisection are (5, –3) and (3, –4).