Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).
The coordinates of the points of trisection are (2, -5/3) and (0, -7/3).
Explanation
This question is directly solved in Exercise 7.2, Question 2. Following the method shown in Example 8 of the textbook, points of trisection divide the line segment into three equal parts. The first point divides the segment in ratio 1:2, and the second point divides it in ratio 2:1. The section formula is applied to find each coordinate.
Solution Steps
Step 1: Let P and Q be the points of trisection of the line segment joining A(4, -1) and B(-2, -3). Therefore, AP = PQ = QB.
Step 2: Point P divides AB internally in the ratio 1:2. Using the section formula: P = ((1(-2) + 2(4))/(1+2), (1(-3) + 2(-1))/(1+2)) P = ((-2 + 8)/3, (-3 - 2)/3) P = (6/3, -5/3) = (2, -5/3)
Step 3: Point Q divides AB internally in the ratio 2:1. Using the section formula: Q = ((2(-2) + 1(4))/(2+1), (2(-3) + 1(-1))/(2+1)) Q = ((-4 + 4)/3, (-6 - 1)/3) Q = (0/3, -7/3) = (0, -7/3)
Step 4: Therefore, the coordinates of the points of trisection are (2, -5/3) and (0, -7/3).