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The constellation of Pegasus is named after the winged horse in Greek mythology. According to the myth, when Perseus killed the Gorgon Medusa (whose hair was made of snakes), Pegasus was born from her blood.

In the constellation of Pegasus, the horse's body is represented by four stars called "The Great _____".

The stars at the corners of this quadrilateral can be drawn on a Cartesian plane at $A (- 1, 5), B (3, 2), C (0, - 2), D (- 4, 1)$ .

Choose the correct property of the sides of the quadrilateral.

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Important Questions on Coordinate Geometry

EASY

Mathematics>Geometry>Coordinate Geometry>Distance Formula

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

EASY

Mathematics>Geometry>Coordinate Geometry>Distance Formula

The equation of the graph shown here is:

Question Image

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Distance Formula

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>Coordinate Geometry>Distance Formula

In the given figure, $A P$ bisect $∠ B A C$ . If $AB = 4 cm, AC = 6 cm$ and $BP = 3 cm$ , then the length of $CP$ is:

Question Image

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Distance Formula

Let

A B C D

be a square of side length

1

, and

Γ

a circle passing through

B

and

C

, and touching

A D

. The radius of

Γ

EASY

Mathematics>Geometry>Coordinate Geometry>Distance Formula

The points

(a, b + c), (b, c + a), (c, a + b)

are the vertices of which of the following?

HARD

Mathematics>Geometry>Coordinate Geometry>Distance Formula

If the distance between the points

(x, 0)

and

(- 7, 0)

10

. Then, the possible values of

x

are ______.

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Distance Formula

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

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Distance Formula

Find the area of the triangle formed with the three straight lines represented by:

$(i) x + y = 0 (i i) 3 x = 5 y; a n d (i i i) y = 3 x - 12$

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Distance Formula

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

EASY

Mathematics>Geometry>Coordinate Geometry>Distance Formula

△ 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>Coordinate Geometry>Distance Formula

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

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Distance Formula

What is the area (in square units) of the triangular region enclosed by the graphs of the equations

x + y = 3, 2 x + 5 y = 12

and the

x

-axis?

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Distance Formula

Let

x_{0}, y_{0}

be fixed real numbers such that

x_{0}^{2} + y_{0}^{2} > 1

. If

x, y

are arbitrary real numbers such that

x^{2} + y^{2} \leq 1,

then the minimum value of

{(x - x_{0})}^{2} + {(y - y_{0})}^{2}

HARD

Mathematics>Geometry>Coordinate Geometry>Distance Formula

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>Coordinate Geometry>Distance Formula

The points

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

and

(5, 8, 7)

are

EASY

Mathematics>Geometry>Coordinate Geometry>Distance Formula

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

HARD

Mathematics>Geometry>Coordinate Geometry>Distance Formula

Find the area of the triangle formed by the lines

x - 3 y = 0, x - y = 4

and

x + y = 4 .

HARD

Mathematics>Geometry>Coordinate Geometry>Distance Formula

Let

A B C D

be a square of side length

1 .

Let

P, Q, R, S

be points in the interiors of the sides

A D, B C, A B, C D

respectively, such that

P Q

and

R S

intersect at right angles. If

P Q = \frac{3 \sqrt{3}}{4},

then

R S

equals

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Distance Formula

Let

A = (a_{1}, a_{2})

and

B = (b_{1}, b_{2})

be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between

A

and

B

Important Questions on Coordinate Geometry

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