## Worksheet on Quadrants

We know there are four quadrants in a regular cartesian co-ordinate; in math worksheet on quadrants we will practice the basic questions on quadrants.

**Recall the process to solve the questions given in the worksheet on quadrants;**

**x, y** are real and positive then the point

Having co-ordinate ** (x, y) ** lies in the first quadrant,

Having co-ordinate ** (-x, y) ** lies in the second quadrant,

Having co-ordinate ** (-x, -y) ** lies in the third quadrant,

Having co-ordinate ** (x, -y) ** lies in the fourth quadrant.

1. In which quadrant do the following points lie?

(I) (2, - 7)

(ii) (√5 - 3, - 2)

(iii) (√2 - 1, 3 -√3)

(Iv) (- 5, √7- 2)

(v) (x, y).

2. Points Q, R and S lie on 1st, 2nd, 3rd and 4th quadrants respectively. If dm Minima of each of them from the co-ordinate axes be 6 and 4 units irspritively, write down their co-ordinates.

3. What do you mean by rectangular Cartesian co-ordinates of a point? What do you know about co-ordinates of points lying on x-axis and y-axis? Where do the following points lie?

(i) (4, 0) (ii) (0, - 6) (iii) (0, 3) (iv) (- 5, 0).

4. The sides of the rectangle ABCD are parallel to the co-ordinate axes. If the co-ordinates of the vertices B and D be (7, 3) and ( 2, 6) respectively, find the co-ordinates of the vertices A and C.

Answers for the worksheet on quadrants are given below to check the exact answers of the above questions.

### Answers:

1. (i) 4th quadrant

(ii) 3rd quadrant

(iii) 1st quadrant

(iv) 2nd quadrant

(v) 1st quadrant if x and y are both positive ; 2nd quadrant if x is negative and y positive ; 3rd quadrant if x and y are both negative ;4th quadrant if x is positive and y negative

2. P(4, 6), Q (-4, 6) ,R (-4, -6),S (4, -6);

3. (i) on positive x-axis

(ii) on positive y-axis

(iii) on positive y-axis

(iv) on positive x-axis;

4. A(2, 3) and C(7, 6);

**●** **Co-ordinate Geometry****What is Co-ordinate Geometry?**

**Rectangular Cartesian Co-ordinates**

**Polar Co-ordinates**

**Relation between Cartesian and Polar Co-Ordinates**

**Distance between Two given Points**

**Distance between Two Points in Polar Co-ordinates**

**Division of Line Segment****: Internal & External**

**Area of the Triangle Formed by Three co-ordinate Points**

**Condition of Collinearity of Three Points**

**Medians of a Triangle are Concurrent**

**Apollonius' Theorem**

**Quadrilateral form a Parallelogram **

**Problems on Distance Between Two Points **

**Area of a Triangle Given 3 Points**

**Worksheet on Quadrants**

**Worksheet on Rectangular – Polar Conversion**

**Worksheet on Line-Segment Joining the Points**

**Worksheet on Distance Between Two Points**

**Worksheet on Distance Between the Polar Co-ordinates**

**Worksheet on Finding Mid-Point**

**Worksheet on Division of Line-Segment**

**Worksheet on Centroid of a Triangle**

**Worksheet on Area of Co-ordinate Triangle**

**Worksheet on Collinear Triangle**

**Worksheet on Area of Polygon**

**Worksheet on Cartesian Triangle**

11 and 12 Grade Math

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