Division of Line Segment in Given Ratio - Class X

Coordinate geometry problems involving division of line segments in given ratios, including internal and external division, division by coordinate axes, and 3D coordinate applications.

16 Questions Published

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Questions

Question 1 Multiple Choice (Single Answer)

ABC is a triangle, the point P is on side BC such that $3\bar{BP}=2\bar{PC}$, the point Q is on the line $\bar{CA}$ such that $4\bar{CQ}=\bar{QA}$. If R is the common point $\bar{AP}$ & $\bar{BQ}$, then the ratio in which the fine joining CR divides $\bar{AB}$ is?

$2:5$
$3:8$
$4:1$
$6:1$

Question 2 Multiple Choice (Single Answer)

The line joining points $(3,5)$ and $(2,7)$ is divided by $X-$ axis in the ratio.

$5:7$
$3:2$
$-5:7$
$-3:2$

Question 3 Multiple Choice (Single Answer)

The point $(\dfrac{7}{4},\dfrac{7}{8})$ divides the line segment joining the points (4,-1) and (-2,4) internally in the ratio 3 : 5.

True
False

Question 4 Multiple Choice (Single Answer)

The ratio in which the point (4, 7) divides the line segment joining (1, 4) and (11, 14) is

2 : 7
3 : 7
4 : 5
3 : 8

Question 5 Multiple Choice (Single Answer)

A square sheet of paper $ABCD$ is so folded that $B$ falls on the mid point $M$ of $CD$. The crease will divide $BC$ in the ratio :

$7:4$
$5:3$
$8:5$
$4:1$

Question 6 Multiple Choice (Single Answer)

Perpendicular from the origin to the line joining the points $(c , cos \alpha, c , sin \alpha)$ and $(c , cos \beta , , c , sin \beta)$ divides it in the ratio

2 : 1
1 : 2
1 : 1
none of these

Question 7 Multiple Choice (Single Answer)

The join of $(4, 5)$ and $(1,2)$ is divided by y-axis in the ratio

$-1:4$
$-4:1$
$-2:1$
$-5:1$

Question 8 Multiple Choice (Single Answer)

The point which divides the line segment joining $(-2, 4), (2, 7)$ in the ratio $2:1$ externally is

$(6, 10)$
$(2, \dfrac{10}{3})$
$(\dfrac{-4}{3}, \dfrac{2}{3})$
$( \dfrac{2}{3} ,6)$

Question 9 Multiple Choice (Single Answer)

Find the points $A(a, b), B(-a, -b)$ and $P(a^2, ab)$ are collinear then the ratio in which p divides $\overline{AB}$ is

1 + a : 1 - a
1 : a
a : 1
1 - a : 1 + a

Question 10 Multiple Choice (Single Answer)

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

$-3$
$\dfrac{-1}{3}$
$3$
$\dfrac{1}{3}$

Question 11 Multiple Choice (Single Answer)

In $\triangle ABC$ $PQR$ $\overline { BC } .\overline { CA } .\overline { AB } $ respectively dividing them in the ratio $1:4,3:2$ and $3:7$. The point $S$ divides $AB$ in the ratio $1:3$ Then $\dfrac { \left| \overline { AP } +\overline { BQ } +\overline { CR } \right| }{ \left| CS \right| } =$

$\dfrac {1}{5}$
$\dfrac {2}{5}$
$\dfrac {5}{2}$
$\dfrac {7}{10}$

Question 12 Multiple Choice (Single Answer)

A straight line through the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at point P and Q respectively. Then the point O divides the segment PQ in the ratio

Question 13 Multiple Choice (Single Answer)

The ratio in which the line segment joining the points $\left(3,-4\right)$ and $\left(-5,6\right)$ is divided by the $x-$ axis, is

$2:3$
$3:2$
$6:4$
$none\ of\ these$

Question 14 Multiple Choice (Single Answer)

The ratio in which the point $(x _{1} \sin^{2} \theta, y _{1} \cos^{2} \theta)$ divides the line joining $(x _{1}, 0)$ and $(0, y _{1})$ is -

$\tan^{2} \theta : \cot^{2} \theta$
$\cos \theta : \sin \theta $
$\cos^{2} \theta : \sin^{2} \theta$
$(1-\cos \theta) : (1-\sin \theta)$

Question 15 Multiple Choice (Single Answer)

A point which divides the joint of $(1,2)$ and $(3,4)$ externally in the ratio $1:1$

Lies in the first quadrant
Lies in the second quadrant
Lies in third quadrat
Cannot be found

Question 16 Multiple Choice (Single Answer)

If the ratio in which the line segment joining the points (6,4) and (x,-7) divided internally by y-axis is 6: 1, then x equals

2
3
-1
-2

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