HARD

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Shown below is a map of Giri's neighbourhood.

Giri did a survey of his neighbourhood and collected the following information.
* The hotel, mall and the main gate of the garden lie in a straight line.
* The distance between the hotel and the mall is half the distance between the mall and the main gate of the garden.
* The bus stand is exactly midway between the main gate of the garden and the fire station.
* The mall, bus stand and the water tank lie in a straight line.

Giri proposed a plan to make a triangular pathway by joining the midpoints of the sides of the triangular garden.
What will be the area, in square units, enclosed by the triangular pathway?

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Important Questions on Co-ordinate Geometry

EASY

Mathematics>Geometry>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section Formula

The equation of the graph shown here is:

Question Image

MEDIUM

Mathematics>Geometry>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section Formula

The points

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

are the vertices of which of the following?

HARD

Mathematics>Geometry>Co-ordinate Geometry>Section Formula

If the distance between the points

(x, 0)

and

(- 7, 0)

10

. Then, the possible values of

x

are ______.

MEDIUM

Mathematics>Geometry>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section Formula

The points

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

and

(5, 8, 7)

are

EASY

Mathematics>Geometry>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section 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>Co-ordinate Geometry>Section 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 Co-ordinate Geometry

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