# Co – ordinate geometry Questions and Answers

## Questions and Answers on Coordinate Geometry

This page deals with different types of Coordinate geometry Questions and Answers which can be asked in placement exams or any other competitive exams which has included Coordinate Geometry in its Syllabus.

Definition of Co-Ordinate Geometry:

Coordinate geometry is a discipline of mathematics that aids in the presentation of geometric forms on a two-dimensional plane and the learning of their characteristics. To get a rudimentary grasp of Coordinate geometry, we will learn about the coordinate plane and the coordinates of a point.

Below the example questions you can further solve Sample Coordinate geometry Questions and Answers.

### Rules

• When the x and y axis intersect at a point then it is called origin. Both x and y tend to be 0.
• The values are positive on the right hand side of the x-axis and the values are negative on the left hand side of x axis.
• The value on the upper side of the y axis tend to be positive and the value below tend to be negative.
• By a set of two numbers a point on the plane can be located. First value will be of x axis and second value will be of y-axis which will determine the unified position on the plane.

Example 1:

Find the equation of straight line passing through (2, 3) and perpendicular to the line 3x + 2y + 4 = 0

Options:

a. y=5/3x- 2
b. 3Y=2x+5
c. 3Y=5x-2
d. None of these

Solution:

The given line is 3x + 2y + 4 = 0 or y = -3x / 2 – 2
Any line perpendicular to it will have slope = 2 / 3
Thus equation of line through (2, 3) and slope 2 / 3 is
$(y – 3) =\frac{2}{3(x – 2)}$
3y – 9 = 2x – 4
3y – 2x – 5 = 0.

Correct Option is b.

Example 2:

Find the coordinate of the point which will divide the line joining the point (2,4) and (7,9) internally in the ratio 1:2?

Options:

a. (5/3 , 1/3)
b. (3/8 , 3/11)
c. (8/3 , 11/3)
d. (11/3 , 17/3)

The internal division will use the formula
$\frac{(mx_2 + nx_1)}{(m + n)}$
$y = \frac{(my_2 + ny_1)}{(m + n)}$.
So, the point becomes (11/3, 17/3).

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Question 1

Time: 00:00:00
Given two points A(-2,0) and B(0, 4), M is a point with coordinates (x, x), x ≥ 0. P divides the joining of A & B in the ratio 2: 1. C & D are the midpoints of BM and AM respectively. Area of the ∆AMB is minimum if the coordinates of M are

(0,0)

(0,0)

(1,1)

(1,1)

(2,2)

(2,2)

(3,3)

(3,3)

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Question 2

Time: 00:00:00
If the centroid of a triangle formed by (7, x), (y, –6), and (9, 10) is (6, 3), then the values of x and y are respectively.

5,2

5,2

2,5

2,5

1,0

1,0

0,0

0,0

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Question 3

Time: 00:00:00
(0, 0, 0) (a, 0, 0), (0, b, 0) and (0, 0, c) are four distinct points. What are the coordinates of the point which is equidistant from the four points?

((a+b+c)/3, (a+b+c)/3, (a+b+c)/3)

((a+b+c)/3, (a+b+c)/3, (a+b+c)/3)

(a, b, c)

(a, b, c)

(a/3, b/3, c/3)

(a/3, b/3, c/3)

(a/2, b/2, c/2)

(a/2, b/2, c/2)

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Question 4

Time: 00:00:00
What is the ratio in which the point C(-2/7,-20/7) divides the line joining the points A(–2, –2) and B(2, –4)?

1 : 3

1 : 3

3 : 4

3 : 4

1 : 2

1 : 2

2 : 3

2 : 3

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Question 5

Time: 00:00:00
The co-ordinates of incentre of ∆ ABC with vertices A(0, 6), B(8, 12), and C(8, 0) is.

(5, 6)

(5, 6)

(–4, 3)

(–4, 3)

(8, 11)

(8, 11)

(16/3,0)

(16/3,0)

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Question 6

Time: 00:00:00
If t₁ ≠ t₂ and the points A (a, 0), B (at₁², 2at₁) and C (at₂², 2at₂) are collinear, then t t is equal to

1

1

-1

-1

2

2

-2

-2

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Question 7

Time: 00:00:00
The area of quadrilateral ABCD whose vertices in order are A(1, 1), B(7, –3), C(12, 2) and D(7, 21) is

66 sq units

66 sq units

132 sq units

132 sq units

124 sq units

124 sq units

86.5 sq units

86.5 sq units

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Question 8

Time: 00:00:00
The vertices of a triangle ABC are A (2, 3, 1), B (–2, 2, 0), and C(0, 1, –1). What is the magnitude of the line joining mid points of the sides AC and BC?

1/√2 unit

1/√2 unit

1 unit

1 unit

3/√2 unit

3/√2 unit

2 unit

2 unit

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Question 9

Time: 00:00:00
What is the reflection of the point (1.6, 5) in the line y = 1.4?

(1.6, 2.2)

(1.6, 2.2)

(1.6, –1.4)

(1.6, –1.4)

(1.6, –3.6)

(1.6, –3.6)

(1.6, –2.2)

(1.6, –2.2)

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Question 10

Time: 00:00:00
A Rod is placed in two-dimensional Co-ordinate plane and co-ordinate of its ends are A=(6, – 4) and B=(0, 8). A carpenter wants to cut this road in 5:1. What are the co-ordinates of that point where he should cut?

(–1, 6)

(–1, 6)

(1, 6)

(1, 6)

(–1, –6)

(–1, –6)

(1, –6)

(1, –6)

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Question 11

Time: 00:00:00
If a vertex of a triangle is (1, 1) and the midpoints of two sides of the triangle through this vertex are (–1, 2) and (3, 2), then the centroid of the triangle is

$(1, \frac{7}{3})$

$(1, \frac{7}{3})$

$\left ( \frac{-1}{3}, \frac{7}{3} \right )

\left ( \frac{-1}{3}, \frac{7}{3} \right )

(-1, \frac{7}{3})$

$(-1, \frac{7}{3})$

$\left ( \frac{1}{3} , 7/3)$

$\left ( \frac{1}{3} , 7/3)$

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Question 12

Time: 00:00:00
The incentre of the triangle with vertices A(1, √3), B (0, 0) and C(2, 0) is

$(1, \frac{\sqrt3}{2})$

$(1, \frac{\sqrt3}{2})$

$(1, \frac{1}{\sqrt{3}})$

$(1, \frac{1}{\sqrt{3}})$

$\left ( \frac{2}{3}, \frac{\sqrt{3}}{2} \right )$

$\left ( \frac{2}{3}, \frac{\sqrt{3}}{2} \right )$

$\left ( \frac{2}{3}, \frac{1}{\sqrt{3}} \right )$

$\left ( \frac{2}{3}, \frac{1}{\sqrt{3}} \right )$

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Question 13

Time: 00:00:00
If the three consecutive vertices of a parallelogram are (–2, –1), (1, 0) and (4, 3), then what are the coordinates of the fourth vertex?

(1, 2)

(1, 2)

(1, 0)

(1, 0)

(0, 0)

(0, 0)

(1, –1)

(1, –1)

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Question 14

Time: 00:00:00
The points (5, 1), (1, –1) and (11, 4) are

vertices of an isosceles triangle

vertices of an isosceles triangle

vertices of a right-angled triangle

vertices of a right-angled triangle

collinear

collinear

vertices of an equilateral triangle

vertices of an equilateral triangle

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Question 15

Time: 00:00:00
A (– 2, – 1), B (1, 0), C (4, 3), and D (1,2) are the four points of a quadrilateral. The quadrilateral is a :

Parallelogram

Parallelogram

Rhombus

Rhombus

Square

Square

None of (a), (b), (c)

None of (a), (b), (c)

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Question 16

Time: 00:00:00
The point (–2, 3) lies in the quadrant:

Second

Second

First

First

Third

Third

Fourth

Fourth

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Question 17

Time: 00:00:00
Let the vertices of a triangle ABC be (4, 3), (7, –1), (9, 3) then the triangle is:

Isosceles

Isosceles

Equilateral

Equilateral

Scalene

Scalene

None of the above

None of the above

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