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A variable line in a plane passes through a fixed point and meets the coordinate axes at points $A$ and $B$ . Then the locus of the mid-point of $A B$ is

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Important Questions on Straight Lines and Quadratic Equations

EASY

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

P (8, 10)

and

Q (14, - 2)

are two given points and the point

R

divides the line-segment

P Q

externally in the ratio

8 : 6

. The coordinates of

R

are

EASY

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

△ ABC, D, E

and

F

are the midpoints of the sides AB, BC and CA, respectively. If

AB = 12 cm, BC = 20 cm

and

CA = 15 cm

, then the value of

\frac{1}{2} (DE + EF + DF)

is:

MEDIUM

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

If the equation of a line which divides the line segment joining the points

(1, 0)

and

(3, 0)

in the ratio

2 : 1

and is also perpendicular to it, is

a x = 7

, then the value of

a

is equal to

EASY

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

If the points

(2, 4, - 1), (3, 6, - 1)

and

(4, 5, 1)

are three consecutive vertices of a parallelogram, then its fourth vertex is

MEDIUM

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

A triangle has a vertex at

(1, 2)

and the mid points of the two sides through it are

(- 1, 1)

and

(2, 3)

. Then the centroid of this triangle is:

EASY

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

The ratio in which the straight line

3 x + 4 y = 6

divides the join of the points

(2, - 1)

and

(1, 1)

HARD

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

Let

S

be the focus of parabola

x^{2} + 8 y = 0

and

Q

be any point on it. If

P

divides the line segment

S Q

in the ratio

1 : 2,

then the locus of

P

EASY

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

Find the coordinates of a point

A

, where

A B

is diameter of a circle whose centre is

(2, - 3)

and

B

is the point

(1, 4)

MEDIUM

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

O P Q R

is a square and

M, N

are the middle points of the sides

P Q

and

Q R

respectively, then the ratio of the areas of the square and

Δ O M N

MEDIUM

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

P (- 3, - 2, 4), Q (- 9, - 8, 10)

and

R (- 5, - 4, 6)

are collinear, then the ratio in which

R

divides

P Q

EASY

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

If the portion of a straight line intercepted between the coordinate axes is divided by the point

(2, 3)

in the ratio

2 : 3

then the product of the intercepts made by this line on the axes is

EASY

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

The coordinate of the point dividing internally the line joining the points

(4, - 2)

and

(8, 6)

in the ratio

7 : 5

MEDIUM

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

Find the ratio in which the segment joining the point

(1, - 3)

and

(4, 5)

is divided by

x ‐

axis? Also, find the coordinates of this point of the

x ‐

axis.

EASY

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

The points

(2, 3, 4), (- 1, - 2, 1)

and

(5, 8, 7)

are

HARD

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

If $A (- 2, 1), B (a, 0), C (4, b)$ and $D (1, 2)$ are the vertices of a parallelogram $A B C D,$ find the values of $a$ and $b .$ Hence, find the length of its sides.

HARD

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

The line segment joining the points

A (2, 1)

and

B (5, - 8)

is trisected at the points

P

and

Q

such that

P

is nearer to

A

. If

P

also
lies on the line given by

2 x - y + k = 0

, then find the value of

k

EASY

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

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

EASY

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

A straight line through the origin

O

meets the parallel lines

4 x + 2 y = 9

and

2 x + y + 6 = 0

P

and

Q

respectively. The point

O

divides the segment

P Q

in the ratio

MEDIUM

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

Find the ratio in which line $3 x + 2 y = 17$ divides the line segment joined by points $(2, 5)$ and $(5, 2) .$

MEDIUM

Mathematics>Geometry>Straight Lines and Quadratic Equations>Length of a Line Segment

In a

∆ A B C

, medians,

A D

and

B E

are drawn. If

A D = 4

∠ D A B = \frac{π}{6} a n d ∠ A B E = \frac{π}{3}

, then the area of the

∆ A B C

A variable line in a plane passes through a fixed point and meets the coordinate axes at points A and B. Then the locus of the mid-point of AB is

Important Questions on Straight Lines and Quadratic Equations

Learn and Prepare for any exam you want !

A variable line in a plane passes through a fixed point and meets the coordinate axes at points $A$ and $B$ . Then the locus of the mid-point of $A B$ is