Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 5

EASY

JEE Main/Advance

IMPORTANT

Earn 100

In which ratio $P (2 a - 2, 4 a - 6)$ divides $Q (2 a - 3, 3 a - 7)$ and $R (2 a, 6 a - 4)$ .

Important Questions on Point and Straight Line

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 6

(i)

Find the value of

λ

such that points

P (1, 2), Q (- 2, 3)

and

R (λ + 1, λ)

are not forming a triangle?

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 7

(ii)

Find the ratio in which the line segment joining of the points

(1, 2)

and

(- 2, 3)

is divided by the line

3 x + 4 y = 7

.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 8

Find the harmonic conjugate of the point

R (5, 1)

with respect to points

P (2, 10)

and

Q (6, - 2)

.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 9

A

and

B

are the points

(3, 4)

and

(5, - 2)

respectively. Find the co-ordinates of a point

P

such that

P A = P B

and the area of the triangle

P A B = 10

sq.units.

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 10

Find the area of the quadrilateral with vertices as the points given in following:

(0, 0), (4, 3), (6, 0), (0, 3)

.

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 11

Find the area of the quadrilateral with vertices as the points given in following:

(0, 0), (a, 0), (a, b), (0, b)

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 12

Reduce

x + \sqrt{3} y + 4 = 0

to the

(i)

Slope intercepts form and find its slope and

y

-intercept.

(ii)

Intercepts form and find its intercepts on the axes.

(iii)

Normal form and find values of

P

and

α

.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 13

Find the number of straight lines passing through

(2, 4)

and forming a triangle of

16 sq

.

cm

with the coordinate axis.