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JEE • MATHEMATICS • 2D GEOMETRY SYSTEM

2d geometry system practice · Easy

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These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 1-30 of 128 questions

1 Easy

1 of 128

Application +4 | -1

The incentre of the triangle with vertices

(1, \sqrt{3}),(0,0)

and

(2,0)

View answer and explanation

Correct option: D

(1,1 / \sqrt{3})

Option D (1, 1/

\sqrt{3}

) is correct because the triangle is equilateral, so the incenter coincides with the centroid, which is easily calculated.

2 Easy

2 of 128

Application +4 | -1

The triangle with vertex

(1,5),(-3,1) \,\&\,(-2,1)

View answer and explanation

Correct option: D

None of these

Option D (None of these) is correct because the triangle's side lengths do not satisfy the conditions for being isosceles, equilateral, or a right-angled triangle.

3 Easy

3 of 128

Application +4 | -1

The area of the quadrilateral with its vertices at the foci of the conics

9 x^2-16 y^2-18 x+32 y-23

=0

and

25 x^2+9 y^2-50 x-18 y+33=0

, is

View answer and explanation

Correct option: B

\frac{8}{9}

Option B

\frac{8}{9}

is correct because calculating the foci of both conics and then finding the area of the quadrilateral formed by them gives this result.

4 Easy

4 of 128

Application +4 | -1

Orthocentre of the triangle whose vertices are

(0,0)(3,0)

and

(0,4)

View answer and explanation

Correct option: A

(0,0)

Option A (

(0,0)

) is correct because the orthocenter of a right-angled triangle is the vertex at the right angle, which is the origin in this case.

5 Easy

5 of 128

Analyzing +4 | -1

A triangle

A B C

with vertices

A(-1,0), B\left(-2, \frac{3}{4}\right)

and

C\left(-3,-\frac{7}{6}\right)

has its orthocentre at

H

. Then, the orthocentre of triangle

B C H

will be

View answer and explanation

Correct option: D

None of these

Option D (None of these) is correct because the orthocenter of triangle BCH is actually vertex A(-1, 0).

6 Easy

6 of 128

Application +4 | -1

If the vertices of a triangle be

(a, b-c),(b, c-a)

and

(c, a-b)

, then the centroid of the triangle lies

View answer and explanation

Correct option: B

x

-axis

Option B (On

x

-axis) is correct because the y-coordinate of the centroid is 0, indicating that it lies on the x-axis.

7 Easy

7 of 128

Application +4 | -1

The greatest angle of a cyclic quadrilateral is 3 times the least. The circular measure of the least angle is

View answer and explanation

Correct option: B

\frac{\pi}{4}

Option B (

\frac{\pi}{4}

) is correct because in a cyclic quadrilateral, opposite angles are supplementary. If the greatest angle is 3 times the least, then the least angle is 45 degrees, which is

\frac{\pi}{4}

radians.

8 Easy

8 of 128

Application +4 | -1

The distance between points

P(-3,-2)

and

Q(-6,7)

, the axes being inclined at

60^{\circ}

, is

View answer and explanation

Correct option: A

3 \sqrt{7}

Option A (

3 \sqrt{{7}}

) is correct because it represents the distance between the points when the axes are inclined at 60 degrees.

9 Easy

9 of 128

Application +4 | -1

The points

(k-1, k+2),(k, k+1),(k+1, k)

are collinear for

View answer and explanation

Correct option: A

any value of

k

Option A (any value of

k

) is correct because the slope between any two points is independent of k, indicating collinearity for all k.

10 Easy

10 of 128

Application +4 | -1

A B C D

is a quadrilateral.

P(3,7)

and

Q(7,3)

are the middle points of the diagonals

A C

and

B D

respectively. The coordinates of the mean point (or the centre of mean position) of the vertices of the quadrilateral are

View answer and explanation

Correct option: C

(5,5)

Option C (5,5) is correct because the coordinates of the mean point are the midpoint of the line segment joining the midpoints of the diagonals.

11 Easy

11 of 128

Application +4 | -1

(4 x+3, y)=(3 x+5,-2)

, then the sum of the values of

x

{y}

View answer and explanation

Correct option: A

Option A (0) is correct because solving the equations yields x = 2 and y = -2, so x + y = 0.

12 Easy

12 of 128

Application +4 | -1

One of the diameter of the circle circum scribing the rectangle

\mathrm{ABCD}

4 y=x+7

. If

\mathrm{A}

and B are points

(-3,4) \&(5,4)

respectively. Then the area of the rectangle is (In Sq units)

View answer and explanation

Correct option: D

Option D (32) is correct. By finding the center of the circumscribing circle and using the given points, the dimensions of the rectangle can be determined, leading to the area.

13 Easy

13 of 128

Application +4 | -1

P

and

Q

are two points whose coordinates are

\left(a t^2, 2 a t\right)

and

\left(\frac{a}{t^2},-\frac{2 a}{t}\right)

respectively and

S

is the point

(a, 0)

. Then, harmonic mean of

S P

and

S Q

, is

View answer and explanation

Correct option: C

2 a

Option C (

2a

) is correct because it represents the harmonic mean of the distances SP and SQ.

14 Easy

14 of 128

Understanding +4 | -1

If the point

\left(x_1+t\left(x_2-x_1\right), y_1+t\left(y_2-y_1\right)\right)

divides the join of

\left(x_1, y_1\right)

and

\left(x_2, y_2\right)

internally, then

View answer and explanation

Correct option: B

0 < t < 1

Option B (

0 < t < 1

) is correct because for internal division, the ratio must be positive and finite, implying t lies between 0 and 1.

15 Easy

15 of 128

Application +4 | -1

The incentre of the triangle with vertices

(1, \sqrt{3}),(0,0)

and

(2,0)

View answer and explanation

Correct option: D

\left(1, \frac{1}{\sqrt{3}}\right)

Option D

\left(1, \frac{1}{\sqrt{3}}\right)

is correct because the triangle is equilateral, making the incenter the same as the centroid, which is easily calculated.

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16 Easy

16 of 128

Application +4 | -1

The mid points of the sides

A B

and

A C

of a triangle

A B C

are

(2,-1)

and

(-4,7)

respectively, then the length of

B C

View answer and explanation

Correct option: B

Option B (20) is correct because the length of BC is twice the length of the line segment joining the midpoints of AB and AC.

17 Easy

17 of 128

Application +4 | -1

If the distance between the points

(x, 2)

and

(3,4)

is 2 , then the value of

x

View answer and explanation

Correct option: C

Option C (3) is correct because it is the value of

x

that satisfies the given distance condition.

18 Easy

18 of 128

Application +4 | -1

Let the area of the triangle with vertices

A(1,\alpha ),\,\,\,\,B(\alpha ,0)\,\,\,{\text{and}}\,\,\,\,\,C(0,\alpha )

be 4 sq units. If the points

(\alpha , - \alpha ),\,\,\,( - \alpha ,\alpha )\,\,\,\,{\text{and}}\,\,\,({\alpha ^2},\beta )

are collinear, then

\beta

is equal to

View answer and explanation

Correct option: C

-64

Option C (-64) is correct because by calculating the area of the triangle and using the collinearity condition, we can find the value of

\beta

19 Easy

19 of 128

Application +4 | -1

O

is the origin and

A

is the point

(3,4)

. If a point

P

moves so that the line segment

O P

is always parallel to the line segment

O A

, then the equation to the locus of

P

View answer and explanation

Correct option: A

4 x-3 y=0

Option A (

4x - 3y = 0

) is correct because the locus of point P, where OP is parallel to OA, results in a linear equation representing a straight line through the origin with the same slope as OA.

20 Easy

20 of 128

Understanding +4 | -1

The points

(a, b),(c, d)

and

\left(\frac{k c+l a}{k+l}, \frac{k d+l b}{k+l}\right)

are

View answer and explanation

Correct option: D

Collinear

Option D (Collinear) is correct because the third point is a section formula representation, indicating it lies on the line joining the first two points.

21 Easy

21 of 128

Application +4 | -1

The

x

-coordinates of the incentre of the triangle where the mid-points of the sides are

(0,1),(1,1)

and

(1,0)

View answer and explanation

Correct option: C

2-\sqrt{2}

Option C

2-\sqrt{2}

is correct because it is the x-coordinate of the incenter of the triangle formed by the given midpoints.

22 Easy

22 of 128

Application +4 | -1

If area of

\Delta A B C

5 sq. unit where

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

and

C

lies on

y=2 x

then co-ordinate of

C

can be

View answer and explanation

Correct option: A

(-10,-20)

Option A, (-10, -20), is correct because it is one of the possible coordinates for point C on the line y=2x such that the area of triangle ABC is 5 sq. units.

23 Easy

23 of 128

Application +4 | -1

O

is the origin and

P\left(x_1, y_1\right), Q\left(x_2, y_2\right)

are two points

O P \times O Q \sin \angle P O Q=

View answer and explanation

Correct option: C

\left|x_1 y_2-x_2 y_1\right|

Option C (

\left|x_1 y_2-x_2 y_1\right|

) is correct because it represents twice the area of the triangle formed by the origin and the two points P and Q.

24 Easy

24 of 128

Application +4 | -1

Coordinates of the orthocentre of the triangle whose sides are

x=3, y=4

and

3 x+4 y=6

View answer and explanation

Correct option: D

(3,4)

Option D (

(3,4)

) is correct because the orthocentre of a right-angled triangle is the vertex at the right angle, which is the intersection of the lines

x=3

and

y=4

25 Easy

25 of 128

Application +4 | -1

If the centroid and circumcentre of

a

triangle are

(3,3)

and

(6,2)

respectively, then the orthocentre, is

View answer and explanation

Correct option: A

(-3,5)

Option A (-3, 5) is correct because the centroid divides the line joining the circumcenter and orthocenter in the ratio 1:2.

26 Easy

26 of 128

Application +4 | -1

Two vertices of a triangle are

(5,4)

and

(-2,4)

. If its centroid is

(5,6)

then the third vertex has the coordinates

View answer and explanation

Correct option: A

(12,10)

Option A (

(12,10)

) is correct because using the centroid formula, we can solve for the coordinates of the third vertex.

27 Easy

27 of 128

Application +4 | -1

If the points

(k, 2-2 k),(1-k, 2 k)

and

(-k-4,6-2 k)

be collinear, then the possible values of

k

are

View answer and explanation

Correct option: A

\frac{1}{2},-1

Option A (

\frac{1}{2},-1

) is correct because these values of k make the determinant of the matrix formed by the points equal to zero, indicating collinearity.

28 Easy

28 of 128

Application +4 | -1

A point moves in such a way that its distance from

(1,-2)

is always the twice from

(-3,5)

, the locus of the point is

View answer and explanation

Correct option: C

3\left(x^{2}+y^{2}\right)+26 x-44 y+131=0

Option C (

3\left(x^{2}+y^{2}\right)+26 x-44 y+131=0

) is correct because it represents the locus of the point satisfying the given distance condition.

29 Easy

29 of 128

Application +4 | -1

If the area of the triangle with vertices

(x, 0),(1,1)

and

(0,2)

is 4 square units then a value of

x

View answer and explanation

Correct option: A

-2

Option A (-2) is correct because the value of x is found by setting up the determinant equation for the area of a triangle and solving for x.

30 Easy

30 of 128

Analyzing +4 | -1

\alpha_1, \alpha_2, \alpha_3, \beta_1, \beta_2, \beta_3

are the values of

n

for which

\sum\limits_{r = 0}^{n - 1} {{x^{2r}}}

is divisible by

\sum\limits_{r = 0}^{n - 1} {{x^r}} ,

then the triangle having vertices

\left(\alpha_1, \beta_1\right),\left(\alpha_2, \beta_2\right)

and

\left(\alpha_3, \beta_3\right)

cannot be

View answer and explanation

Correct option: D

an equilateral triangle

Option D (an equilateral triangle) is correct because the vertices derived from the given condition do not form an equilateral triangle.

Revision notes and key takeaways

Review 2D GEOMETRY SYSTEM in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 128 single-correct-answer MCQs on 2D GEOMETRY SYSTEM.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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