Trisection of a Line Segment

Q.

Find the coordinates of points which trisect the line segment joining (1, –2) and (–3, 4).

1. (−1/3, 0) and (−5/3, 4)

2. (−1/3, 0) and (−5/6, 2)

3. (−1/2, 0) and (−5/3, 2)

4. (−1/3, 0) and (−5/3, 2)

Q. Question 18
Find the coordinates of the point R on the line segment joining the points P(-1, 3) and Q(2, 5) such that
$PR=\frac{3}{5}PQ.$

Q. The ratio in which the line segment joining P (x₁, y₁) and Q (x₂, y₂) is divided by x-axis is

(a) y₁ : y₂

(b) −y₁ : y₂

(c) x₁ : x₂

(d) −x₁ : x₂

Q.

Find the value of 'a' for which the following points A(a, 3), B(2, 1) and C(5, a) are collinear.

1. 1

2. -1

3. 4

4. -4

Q. Find the co-ordinates of the points of trisection of the line segment joining the points $A(6,-2)$ and $B(-8,10)$.

Q. If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C $\left(\frac{3}{2},\frac{5}{2}\right)$, find x, y.

Q. The midpoint of the line segment joining (3m, 6) and (-4, 3n) is (1, 2m-1). Find the value of m.

Q.

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

1. The points of trisection divide 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. 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).
$\left[2Marks\right]$

Q.

$(2,0)$ is a point on the line joining the points $(2x^2,4x)$ and $(2y^2,4y)$. Then,

1. $\frac{1}{y}=\frac{-1}{x}$

2. $\frac{1}{y}=-x$

3. $x=y$

4. $x=-y$

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. Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts.

Q.

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

1. The points of intersection divide a line into 4 equal parts.

2. The points of trisection divide a line in the ratios of 1 : 2 and 2 : 1.

3. There are 3 points of trisection.

4. The points of trisection need not lie on the line joining the two points.

Q.

Find the coordinates of points which trisect the line segment joining (1, –2) and (–3, 4). [4 MARKS]

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

Q. Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts.

Q. Find the slope of the line which passing through the points
$(a{t}_1^2,2a{t}_1)and(a{t}_2^2,2a{t}_2)$

Q.

The co-ordinates of the point which divides the line joining the points (–1, 7) and (4, –3) in the ratio 2:3 is ________.

1. (1, 3)

2. (-1, 3)

3. (1, -3)

4. (-1, -3)

Q.

Find the coordinates of points of trisection of the line segment joining the points A(-2, 8) and B(4, 12)

1. $\begin{array}{c}P=(8,\frac{5}{3})\\ Q=(4,\frac{5}{9})\end{array}$

2. $\begin{array}{c}P=(4,\frac{5}{3})\\ Q=(9,\frac{2}{3})\end{array}$

3. $\begin{array}{c}P=(0,\frac{28}{3})\\ Q=(2,\frac{32}{3})\end{array}$

4. $\begin{array}{c}P=(9,\frac{4}{3})\\ Q=(4,\frac{9}{5})\end{array}$

Q.

Find coordinates of the points of trisection of the line segment joining the points A(-4, 2) and B (-4, 9).

1. $\begin{array}{c}P=(-4,6)\\ Q=(-4,8)\end{array}$

2. $\begin{array}{c}P=(-4,\frac{20}{3})\\ Q=(-4,\frac{13}{3})\end{array}$

3. $\begin{array}{c}P=(-4,\frac{13}{3})\\ Q=(-4,\frac{20}{3})\end{array}$

4. $\begin{array}{c}P=(4,9)\\ Q=(9,\frac{7}{4})\end{array}$

Q.

The plane$2x-3y+z+6=0$ divides the line segment joining $(2,4,16)\mathrm{and}(3,5,-4)$ in the ratio.

Q.

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

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

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

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

Q.

8. For a given data less than ogive and more than ogive intersect at a point P(x, y). Then what does abscissa of the Point represents

Q.

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

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

Q.

The co-ordinates of the point which divides the line joining the points (–1, 7) and (4, –3) in the ratio 2:3 is ________.

1. (1, 3)

2. (-1, 3)

3. (1, -3)

4. (-1, -3)