MEDIUM

Earn 100

Can we draw a triangle having area zero units?

Important Questions on Coordinate Geometry

HARD

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

Let

A

be the set of all points

(α, β)

such that the area of triangle formed by the points

(5, 6),

(3, 2)

and

(α, β)

12

square units. Then the least possible length of a line segment joining the origin to a point in

A,

is :

HARD

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

Let

A (- 1, 1), B (3, 4)

and

C (2, 0)

be given three points. A line

y = m x, m > 0

, intersects lines

A C

and

B C

at point

P

and

Q

respectively. Let

A_{1}

and

A_{2}

be the areas of

Δ A B C

and

Δ P Q C

respectively, such that

A_{1} = 3 A_{2}

, then the value of

m

is equal to :

EASY

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

If each vertex of a triangle is an integer, then triangle will not be.

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

A (- 5, 7)

B (- 4, - 5)

C (- 1, - 6)

and

D (4, 5)

are the vertices of a quadrilateral, find the area(in

sq . unit

) of the quadrilateral

A B C D

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

Let

S

be the set of all triangles in the

x y

-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in

S

has area

50

sq. units, then the number of elements in the set

S

is:

EASY

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

The area of the triangle formed by the points

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

and

(c, a + b)

will be

EASY

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

The area of the parallelogram formed by the lines

y = m x, y = m x + 1, y = n x

and

y = n x + 1

equals

EASY

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

Find the value of

k

if the points

A (2, 3)

B (4, k)

and

C (6, - 3)

are collinear.

HARD

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

If two straight lines

x - 5 y = 2

and

x + 2 y = 9

, Intersect each other at point

A

and Intersects positive

x - a x i s

on points

B

C

respectively, find out the area of triangle

A B C

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

The area of the triangle formed by the intersection of a line parallel to

X

-axis and passing through

P (h, k),

with the lines

y = x

and

x + y = 2

h^{2}

. The locus of the point

P

EASY

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

The value of

p

, for which the points

A (3, 1)

B (5, p)

and

C (7, - 5)

are collinear is

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle 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>Area of a Triangle Formula

Find the area of triangle $PQR$ formed by the points $P (- 5, 7), Q (- 4, - 5)$ and $R (4, 5)$ .

EASY

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

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

and

C (1, 2)

are three points on

X Y

-plane. If a point

P (x, y)

which moves such that the area of triangle

P A B

is twice the area of the triangle

A B C,

then the locus of the point

P

HARD

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

Find the value of

' p'

for which the given points

(- 3, 9), (2, p)

and

(4, - 5)

are collinear.

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

Find the area of the triangle formed by joining the middle points of the sides of the triangle whose vertices are $(0, - 1), (2, 1)$ and $(0, 3)$ .

HARD

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

Find the area of the quadrilateral whose vertices are $(- 3, 4), (- 5, - 6), (4, - 1)$ and $(1, 2)$ .

EASY

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

(x_{1}, y_{1}), (x_{2}, y_{2})

and

(x_{3}, y_{3})

are the vertices of a triangle whose area is

k

square units, then

{|\begin{array}{l} x_{1} & y_{1} & 4 \\ x_{2} & y_{2} & 4 \\ x_{3} & y_{3} & 4 \end{array}|}^{2}

HARD

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

Find the area of the triangle formed by the lines

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

and

x + y = 4 .

MEDIUM

Mathematics>Geometry>Coordinate Geometry>Area of a Triangle Formula

Consider a triangle

A B C

in the

x y

- plane with vertices

A = (0, 0), B = (1,1) a n d C = (9, 1)

. If the line

x = a

divides the triangle into two parts of equal area, then

a

equals

Can we draw a triangle having area zero units?

Important Questions on Coordinate Geometry

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