Section Formula

Q.

In what ratio does the x-axis divide the join of A(2, -3) and B (5, 6)?

(a) 2 : 3 (b) 3 : 5 (c) 1 : 2 (d) 2 : 1

Q.

In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis ?

Q.

The equation of the line through the point $(0,1,2)$ and perpendicular to the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{-2}$ is

1. $\frac{x}{-3}=\frac{y-1}{4}=\frac{z-2}{3}$

2. $\frac{x}{3}=\frac{y-1}{4}=\frac{z-2}{3}$

3. $\frac{x}{3}=\frac{y-1}{-4}=\frac{z-2}{3}$

4. $\frac{x}{3}=\frac{y-1}{4}=\frac{z-2}{-3}$

Q.

In what ratio does the point $(-4,6)$ divide the line segment joining the points $A(-6,10)$ and $B(3,-8)$?

Q.

Midpoint of the line joining the points ($x_1,y_1$) and ($x_2,y_2$) is $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.

1. True

2. False

Q. Find the coordinates of the point which divides the line segment joining the points $(4,-3)$ and $(8,5)$ in the ratio $3:1$ internally.

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.

If A (–2, –1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram, find the values of a and b.

1. a = 1 and b = 3
2. a = 2 and b = 3
3. a = 1 and b = 1
4. a = 1 and b = 4

Q. If P(9a-2, -b) divides the line segment joining A(3a+1, -3) and B(8a, 5) in the ratio 3:1, find the value of a.
a = ___.

Q. The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is

(a) 2: 1

(b) 1 : 2

(c) −2 : 1

(d) 1 : −2

Q. If X(3, –2) and Y(–4, 2) are two points and A is a point on XY such that XA : XY = 3 : 5, then the sum of the x-coordinate and y-coordinate of A is

1. $\frac{-8}{5}$
   
2. $\frac{4}{5}$
   
3. $\frac{-4}{5}$
   
4. $\frac{8}{5}$
   

Q. PQ is the perpendicular bisector of AB, where A = (–3, 5) and B = (–6, 3). If Q lies on AB, then the coordinates of Q are

1. (-7, 4)
2. (-5, 3)
3. (-8, 3)
4. $(\frac{-9}{2},4)$

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

Q. In what ratio does y-axis divide the line segment joining the points (−4, 7) and (3, −7)? [CBSE 2012]

Q.

The line 2x + y - 4 = 0 divides the line segment joining A(2, -2) and B (3, 7) in the ratio

(a) 2 : 5 (b) 2 : 9 (c) 2 : 7 (d) 2 : 3

Q.

If $a,b,c\&d$ are the unit vectors such that $(a\times b).(c\times d)=1$and $a.c=\frac{1}{2}$, then:

1. $a,b,carenon-coplanar$

2. $a,b,darenon-coplanar$

3. $b,darenon-parallel$

4. $a,dareparallelandb,careparallel$

Q. If the points P, Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B(7, 10) in 5 equal parts, find x, y and p. [CBSE 2015]

Q.

Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also, find the coordinates of the point of division.

Q.

Points P, Q, R and S divide the line segment joining the points A (1, 2) and B(6, 7) into five equal parts. Find the coordinates of the points P, Q and R.

Q.

Let$A(1,-1,2)$ and $B(2,3,-1)$ be two points. If a point $P$divides $AB$ internally in the ratio $2:3$, then the position vector of $P$ is

1. $\frac{1}{\sqrt{5}}\left(i+j+k\right)$

2. $\frac{1}{\sqrt{3}}\left(i+6j+k\right)$

3. $\frac{1}{\sqrt{3}}\left(i+j+k\right)$

4. $\frac{1}{5}\left(7i+3j+4k\right)$

5. None of these

Q.

If the point C (–1, 2) divides internally the line segment joining A (2, 5) and B in ratio 3 : 4, find the coordinates of B.

Q.

The point P which divides the line segment joining the points A(2, 5) and B(5, 2) in the ratio 2 : 3 lies in the quadrant

(a) I (b) II (c) III (d) IV

Q.

The point C (–1, 2) divides the line segment AB in the ratio 3:4, where the coordinates of A is (2, 5). The coordinates of B are___________.

1. (–5, –2)

2. (–4, – 2)

3. (–1, – 2)

4. (5, – 4)

Q. A(9, 20) and B(15, 5) are two end points of a line segment divided by a point P(11, 15). Find the ratio in which the point P divides the line segment AB.

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

Q.

The $xy$ plane divides the line joining the points $(-1,3,4)$and $(2,-5,6)$

1. internally in the ratio $2:3$

2. externally in the ratio $2:3$

3. internally in the ratio $3:2$

4. externally in the ratio $3:2$

Q. If (−2, 3), (4, −3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.

Q. If the distance between the points (5, -2) and (1, a) is 5, find the values of a.

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. Find the third vertex of a triangle, if its two vertices are (-1, 4) and (5, 2) and mid-point of one side is (0, 3).
[4 MARKS]

Q.

M is the mid-point of the line segment joining the points A(0, 4) and B(6, 0). M also divides the line segment OP in the ratio 1 : 3.Find:
(i) co-ordinates of M
(ii) co-ordinates of P
(iii) length of BP