Points of Trisection

Q. Which of the following statements are true about points of trisection?

1. The points of trisection divides a line into 3 equal parts.
2. There are 3 points of trisection.
3. The points of trisection divide a line in the ratios of 1 : 2 and 2 : 1.
4. The points of trisection need not lie on the line joining the two points.

Q. The ratio in which the midpoint of A (12 , 8) and B (4 , 6) divides the points of trisection of the line segment AB is

1. 1 : 1
2. 2 : 1
3. 3 : 1

Q. In a line segment AB, P(2, 1) and Q(6, 2) are the points of trisection. Find the coordinates of A and B (P is closer to A and Q is closer to B).

1. $A(10,3)$ and $B(-2,0)$
2. $A(-2,0)$ and $B(10,3)$
3. $A(-2,3)$ and $B(10,-3)$
4. $A(-2,0)$ and $B(10,0)$

Q. A, B, C and D are four points on the same straight line. The distances between successive points are equal such that AB = BC = CD. If A is (1, -3), C is (4, a) and D is (b, 5), then the values of a and b are :

1. $a=\frac{7}{3}andb=\frac{11}{2}$
2. $a=\frac{4}{3}andb=\frac{7}{2}$
3. $a=\frac{4}{3}andb=\frac{11}{2}$
4. $a=\frac{7}{3}andb=\frac{7}{2}$

Q. Find the ratio in which the midpoint of A(14, 10) and B(2, 4) divides the line joining the points of trisection of the line AB.

1. 1 : 2
2. 2 : 1
3. 3 : 2
4. 1 : 1

Q. Find the co-ordinates of the points of trisection of the segment joining the points A(-7, 4) and B(2, -2).

1. (-4, 0)
2. (-1, 0)
3. (-4, 2)
4. (-2, 0)

Q.

The coordinates of the point of trisection of the line segment joining the points A(4, 8) and B(-2, 4) are

1. $\begin{array}{c}P=(-4,\frac{8}{3})\\ Q=(10,-9)\end{array}$

2. $\begin{array}{c}P=(2,\frac{20}{3})\\ Q=(0,\frac{16}{3})\end{array}$

3. $\begin{array}{c}P=(8,-9)\\ Q=(4,\frac{-2}{3})\end{array}$

4. $\begin{array}{c}P=(4,9)\\ Q=(-5,\frac{4}{5})\end{array}$

Q.

Find the points of trisection of the line segment joining the points A(-4, 3) and B (2, -1).

1. $(-2,\frac{5}{3})\text{and}(2,\frac{1}{3})$
2. $(-2,\frac{5}{3})\text{and}(0,\frac{1}{3})$
3. $(2,\frac{5}{3})\text{and}(0,\frac{1}{3})$
4. $(-2,\frac{5}{3})\text{and}(0,\frac{4}{3})$

Q. Find the ratio in which the midpoint of A(12, 8) and B(4, 6) divides the points of trisection of the line AB.

1. 2 : 1
2. 1 : 2
3. 4 : 1
4. 1 : 1

Q. In a line segment AB, P(2, 1) and Q(6, 2) are the points of trisection. The coordinates of A and B (P is closer to A and Q is closer to B) .

1. A(-2, 0) and B(10, 3)
2. A(10, 3) and B(-2, 0)
3. A(-2, 3) and B(10, -3)
4. A(-2, 0) and B(10, 0)