# Co - ordinate geometry Questions

## Definition of Co - ordinate geometry

The study of geometry using coordinate points is called coordinate geometry. By using this geometry distance between two points can be calculated by dividing the line in m:n ratio or finding midpoint or calculating the area of the triangle in a Cartesian plane.

### 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.

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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