Points of Trisection

Q. In what ratio, does the $x-axis$ divides the line segment joining the points (2, -3) and (5, 6)? [4 MARKS]

Q. The line joining the points A(4, -5) and B(4, 5) is divided by the point P such that AP/AB = 2/5. Find the coordinates of P.

Q. Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3). Hence find m.

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.

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

Q. Two vertices of a triangle are (1, 2), (3, 5) and its centroid is at the origin. Find the coordinates of the third vertex.

Q. Find the points which divide the line segment joining A(-4, 0) and B(0, 6) into four equal parts.

Q. Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by x-axis.
Also, find the point of division. [CBSE 2015]

Q. The ratio in which the line segment joining points A (a₁, b₁) and B (a₂, b₂) is divided by y-axis is

(a) −a₁ : a₂

(b) a₁ : a₂

(c) b₁ : b₂

(d) −b₁ : b₂

Q. If the centroid of the triangle formed by the points (3, −5), (−7, 4), (10, −k) is at the point (k −1), then k =

(a) 3

(b) 1

(c) 2

(d) 4

Q.

Find the points of trisection of the line segment joining the points :

(i) (5, -6) and (-7, 5), (ii) (3, -2) and (-3, -4), (iii) (2, -2) and (-7, 4).

Q.

Show that A (3, -2) is a point of trisection of the line-segment joining the points (2, 1) and (5, -8). Also, find the co-ordinates of the other point of trisection.

Q.

Find the centre of a circle passing through the points (6, − 6), (3, − 7) and (3, 3).

Q.

The mid point P of the line segment joining the points A (-10, 4) and B(-2, 0) lies on the line segment joining the points C (-9, -4) and D(-4, y). Find the ratio in which P divides CD. Also, find the values of y.

Q. The length (in units ) of a line segment intercepted between the coordinate axes by the line joining the points (1, 2) and (3, 4) is

Q.

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

Q.

Show that the line segment joining the points (-5, 8) and (10, -4) is trisected by the co-ordinate axes.

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. Question 9
The point which divides the line segment joining points (7, - 6) and (3, 4) in ratio 1:2 internally lies in the
(A) I quadrant
(B) II quadrant
(C) III quadrant
(D) IV quadrant

Q.

In the given figure P(5, -3) and Q(3, y) are the points of trisection of the line segment joining A(7, -2) and B(1, -5). Then y equals

(a) 2 (b) 4 (c) -4 (d) $\frac{-5}{2}$

Q.

Let P and Q be the point of trisection of the line segment joining the points A(2, -2) and B(-7, 4) such that P is nearer to A. What is the coordinates of P and Q ?

1. $P(-4,2)$
   $Q(-1,0)$

2. $P(-1,0)$
   $Q(-4,2)$

3. $P(-4,-1)$
   $Q(2,0)$

4. $P(-2,0)$
   $Q(-3,2)$

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)

Q.

Find the ratio in which origin divides PQ.Ratio being 1 : ____

Q. Find the centroid of the triangle whose vertices are:

(i) (1, 4) (−1, −1), (3, −2)

(ii) (−2, 3) (2, −1) (4, 0)

Q. If the coordinates of the mid-point of the line segment joining the points (2, 1) and (1, -3) is (x, y). What is the relation between x and y?

1. 6x + y = 8
2. 2x - 5y = 4
3. 3x - y = 5
4. 2x + 1 = 0

Q.

Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are:

(i) y = x, y = 2x and y + x = 6

(ii) y = x, 3y = x, x + y = 8

Q. Find the point which divides the line segment joining the points (2, 5) and (1, -6) in the ratio 2 : 1.

1. $(\frac{1}{3}$, $\frac{-5}{3})$
2. $(\frac{4}{3}$, $\frac{-7}{3})$
3. $(\frac{4}{3}$, $\frac{7}{3})$
4. $(\frac{-7}{3}$, $\frac{4}{3})$

Q.

Show that the line joining the points (2, -3) and (-5, 1) is parallel to the line joining the points (7, -1) and (0, 3) and perpendicular to the line joining (4, 5) and (0, -2).

Q.

Determine, graphically, the vertices of the triangle formed by the lines y = x, 3y = x, x + y = 8.

Q.

Find the co-ordinates of the points of tri-section of the line joining the points (-3, 0) and (6, 6).