A line segment A B is divided internally and externally in the same ratio ( > 1 ) at P and Q respectively and M is mid point of A B . Statement 1 : M P , M B , M Q are in G . P . Statement 2 : AP , AB and AQ are in H P .

STATEMENT 1 is true, STATEMENT 2 is true and STATEMENT 2 is not correct explanation for STATEMENT 1 .

STATEMENT 1 is true, STATEMENT 2 is true and STATEMENT 2 is correct explanation for STATEMENT 1 .

STATEMENT 1 is true, STATEMENT 2 is false.

STATEMENT 1 is false, STATEMENT 2 is true

A square of side a lies above the X -axis and has one vertex at the origin. The side passing through the origin makes an angle α 0 < α < π 4 with the positive direction of X -axis. The equation of its diagonal not passing through the origin is

y cos α + sin α + x cos α - sin α = a

y cos α - sin α - x sin α - cos α = a

y cos α + sin α + x sin α - cos α = a

y cos α + sin α + x sin α + cos α = a

y ( cos α - sin α ) + x ( cos α - sin α ) = a

EASY

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IMPORTANT

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Given a $Δ A B C$ with unequal sides. $P$ is the set of all points which is equidistant from $B & C$ and $Q$ is the set of all point which is equidistant from sides $A B$ and $A C$ . Then $n (P \cap Q)$ equals.

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Important Questions on Point and Straight Line

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 65

A line segment

A B

is divided internally and externally in the same ratio

(> 1)

P

and

Q

respectively and

M

is mid point of

A B

.
Statement

1 :

M P, M B, M Q

are in

G . P .

Statement

2 :

AP, AB

and

AQ

are in

H P .

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 66

Find the area of the triangle formed by the mid points of sides of the triangle whose vertices are

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

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 67

A straight line through

P (1, 2)

is such that its intercept between the axes is bisected at

P

. Its equation is

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 68

The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices

(0, 0), (0, 21)

and

(21, 0)

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 69

The line joining two points

A (2, 0), B (3, 1)

is rotated about

A

in anti-clockwise direction through an angle of

15 °

. The equation of the line in the new position, is

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 70

ln a

∆ A B C,

side

A B

has the equation

2 x + 3 y = 29

and the side

A C

has the equation

x + 2 y = 16 .

If the mid point of

B C

(5, 6),

then the equation of

B C

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 71

A square of side

a

lies above the

X

-axis and has one vertex at the origin. The side passing through the origin makes an angle

α (0 < α < \frac{π}{4})

with the positive direction of

X

-axis. The equation of its diagonal not passing through the origin is

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 72

Find equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of

120 °

with the positive direction of

x

-axis.

Given a ΔABC with unequal sides. P is the set of all points which is equidistant from B & C and Q is the set of all point which is equidistant from sides AB and AC. Then n(P∩Q) equals.

Important Questions on Point and Straight Line

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Given a $Δ A B C$ with unequal sides. $P$ is the set of all points which is equidistant from $B & C$ and $Q$ is the set of all point which is equidistant from sides $A B$ and $A C$ . Then $n (P \cap Q)$ equals.