Section Formula

Q. The ratio in which the point (-4, 6) internally divides the line segment joining (-6, 10) and (3, -8) is

1. 5:2
2. 2:7
3. 2:9

Q.

xy plane divides the line joining the points $(2,4,5)$and$(-4,3,-2)$ in the ratio

1. 3:4

2. 3:5

3. 5:2

4. 1:3

Q.

Find the coordinates of the point which divides the join of $P(2,-1,4)$ and $Q(4,3,2)$ in the ratio $2:3$ (i) internally (ii) externally.

Q. The midpoints of the sides of a triangle are (1, 5, -1), (0, 4, -2) and (2, 3, 4). Find its vertices.

Q.

A point R with x-coordinate 4 lies on the line segment joining the points $P(2,-3,4)$ and $Q(8,0,10).$ Find the coordinates of the point R.

Q.

Find the ratio in which the YZ-plane divides the line segment formed by joining the points $(-2,4,7)$ and $(3,-5,8).$

Q.

Find the coordinates of the points which trisect the line segment joining the points $P(4,2,-6)$ and $Q(10,-16,6).$

Q.

A(3, 2, 0) , B(5, 3, 2) and C(-9, 6, -3) are three points joining a triangle and AD is bisector of the angle $\angle$ BAC. AD meets BC at the point

1. $(\frac{19}{8},\frac{-57}{16},\frac{17}{16})$

2. $(\frac{-19}{8},\frac{57}{16},\frac{17}{16})$

3. $(\frac{19}{8},\frac{57}{16},\frac{17}{16})$

4. None of these

Q. Using section formula, prove that the three points A(-2, 3, 5), B(1, 2, 3) and C(7, 0, -1) are collinear.

Q.

Direction ratio of the normal to the plane passing through the points $(0,1,1),(1,1,2)$ and $(-1,2,-2)$ ?

1. $(1,1,1)$

2. $(2,1,-1)$

3. $(1,2,-1)$

4. $(1,-2,-1)$

Q.

Three vertices of a parallelogram PQRS are P(3, - 1, 2), Q (1, 2, - 4) and R (- 1, 1, 2). Find the coordinates of the fourth vertex.

1. (-1, -2, 8)

2. (1, -2, 8)

3. (1, -2, -8)

4. (1, 2, 8)

Q.

If the coordinates of the points A, B, C, be (4, 4), (3, -2) and (3, -16) respectively, then the area of the triangle ABC is

1. 27

2. 15

3. 18

4. 7

Q.

The coordinates of centroid of triangle whose vertices are A(-1, -3), B(5, -6) and C(2, 3) and origin gets shifted to (1, 2) :

1. (4, -1)

2. (2, -2)

3. (0, 0)

4. (-1, 4)

Q.

If coordinates of the points A and B are (2, 4) and (4, 2) respectively and point M is such that A-M-B also AB =

3 AM, then the coordinates of M are

1. 

2. 

3. 

4. 

Q.

$A(3,2,0),B(5,3,2),C(-9,6,-3)$ are three points forming a triangle. If AD, the bisector of $\angle BAC$ meets BC in D, then coordinates of D are _____

1. $(\frac{-19}{8},\frac{57}{16},\frac{17}{16})$

2. $(\frac{19}{8},\frac{-57}{16},\frac{17}{16})$

3. $(\frac{19}{8},\frac{57}{16},\frac{17}{16})$

4. $(\frac{19}{8},\frac{57}{16},\frac{17}{16})$

Q. Find the ratio in which the line segment, joining the points P(2, 3, 4) and Q(-3, 5, -4) is divided by the yz-plane. Also, find the point of intersection.

Q. Find the ratio in which the join of A(2, 1, 5) and B(3, 4, 3) is divided by the plane 2x+2y-2z=1. Also, find the coordinates of the point of division.

Q.

The plane XOZ divides the join of (1, -1, 5) and (2, 3, 4) in the ratio $\lambda :1$ then $\lambda$ is [JET 1988]

1. 3

2. $-\frac{1}{3}$

3. $\frac{1}{3}$

4. -3

Q. 128.If the given points A(3, 2, -4) , B(5, 4, -6) and C(9, 8, -10) are collinear, then the ratio in which A divides BC is = ?

Q. The equation of the internal bisector of $\angle$BAC of $\Delta$ABC with vertices A(5, 2), B(2, 3) and C(6, 5), is

1. 2x + y + 12 = 0

2. x + 2y – 12 = 0

3. 2x + y – 12 = 0

4. 2x + y – 12 = 0

Q.

If the coordinates of the points A, B, C, be (4, 4), (3, -2) and (3, -16) respectively, then the area of the triangle ABC is [MP PET 1982]

1. 27

2. 15

3. 7

4. 18

Q.

If z = x + i y, then the area of the triangle whose vertices are points z, iz and z + iz is

1. 

2. 

3. 2

4. 

Q.

Let A(2, 1, -3) and B(5, -8, 3) be two given points. Find the coordinates of the points of trisection of the line segment AB.

Q.

Find the coordinates of a point which divides the line segment joining the points (5, 4, 2) and (-1, -2, 4) in the ratio

(i) 2 :3 internally.

(ii) 2 :3 externally.

Or

Find the points on Z-axis which are at a distance $\sqrt{21}$ from the point (1, 2, 3).

Q. The ratio in which $\hat{i}+2\hat{j}+3\hat{k}$ divides the join of $-2\hat{i}+3\hat{j}+5\hat{k}$ and $7\hat{i}-\hat{k}$ is

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

Q.

The ratio in which the point R (1, 2) divides the line segment joining points P (2, 3) and Q (3, 5) is:

1. 1 : 2, externally

2. 2 : 1, externally

3. 1 : 2, internally

4. 2 : 1, internally

Q. 64. The equation of the parabola with latus rectum joining the points ( 3 , 5 ) and ( 3 , -3) is __________.

Q.

Find the equation of circle which touches $2x-y+3=0$ and pass through the points of intersection of the line $x+2y-1=0$ and the circle $x^2+y^2-2x+1=0$

1. 

2. 

3. 

4. 

Q. If $A(4,1),B(7,4),C(13,-2)$ are the three consecutive vertices of a rectangle $ABCD$, then the coordinates of $D$ are

1. $(10,5)$
2. $(-10,5)$
3. $(10,-5)$
4. $(-10,-5)$

Q. Point R ( h, k ) divides a line segment between the axes in the ratio 1:2. Find equation of the line.