## Coordinate Geometry - Important Points

1. Each point on a number line is associated with a number called its

**coordinate**.
2. Each point on a plane is associated with an ordered pair (x,y) of numbers called its

**coordinates**.
3. The coordinates of a point on a plane are determined by the point's position relative to two perpendicular number lines called

**axes**.
4. These axes form a

**rectangular coordinate**system.
5. The horizontal line is called the

**x -axis**, and the vertical line is called the**y - axis**.
6. The point of intersection of the axes is called the

**origin**.
7. The plane along the x-axis and y-axis is known as a

**Cartesian plane**to honour the great work of**Rene Descartes**. It is also called**rectangular coordinate plane**or**xy-plane**.
8. The

**positive numbers**appear to the right of the origin on the x-axis and above the origin on the y-axis.
9. The axes divide the plane into four regions called

**quadrants**, which are numbered**counter-clockwise**.
10. The first number in an ordered pair is called the

**x-coordinate**or**abscissa**. The second number is called**y-coordinate**or**ordinate**.XY-coordinates (source:wikipedia) |

11. The symbol P(x,y) denotes that x and y are the coordinates of the point P.

- the abscissa of point P: perpendicular distance of P from the y-axis.
- the ordinate of point P: perpendicular distance of P from the x-axis.

As shown above say P(2,3) represents a perpendicular distance of 2 units from y-axis and 3 units from the x-axis.

12. The abscissa of any point P is

**positive**for points on the**right**of the y-axis,**zero**on the y-axis and**negative**for the points on the left of the y-axis.
13. The ordinate of P is

**positive**for points**above**the x-axis,**zero**on the x-axis, and**negative**for points**below**the x-axis.
14. The

**origin**O has coordinates**(0, 0)**.
15. Any point on the x–axis has its y–coordinate 0. Its coordinates are (x, 0)

16. Any point on the y–axis has its x–coordinate 0. Its coordinates are (0, y)

17. All points on a line parallel to x-axis have the

**same y-coordinate**. (as shown in figure red-line)
18. All points on a line parallel to y-axis have the

**same x-coordinate**. (as shown in fig. with green line)
19. If x ≠ y, then (x, y) ≠ (y, x), and (x, y) = (y, x), if x = y.

20. If P(x1 ,y1) and Q(x2, y2) are any two points in the Cartesian plane, then

- the
**horizontal distance**between P and Q is |x2 - x1| - the
**vertical distance**between P and Q is |y2 -y1|

**Q1: Name the quadrants in which the following points lie**

a. (2,5)

b. (-3,2)

c. (-2, -5)

d. (2, -3)

e. (0, -5)

f. (-3, -9)

g. (3, -3)

h. (-8, 4)

i. (4, 0)

Answer:

a. (2,5) - First

b. (-3,2) - Second

c. (-2, -5) - Third

d. (2, -3) - Fourth

e. (0, -5) - y-axis

f. (-3, -9) - Third

g. (3, -3) - Fourth

h. (-8, 4) - Second

i. (4, 0) - x-axis

**Q2: Write down the coordinates of the paints A, B, C and D as shown in the figure below.**

**Q3: The point whose abscissa is -5 and lies on x-axis is**

(a) (5, 0)

(b) (0, -5)

(c) (0, 5)

(d) (-5, 0)

(b) (0, -5)

(c) (0, 5)

(d) (-5, 0)

Answer: (d) (-5, 0)

(a) I

(b) II

(c) III

(d) IV

Answer: (b) II

(a) Y-axis

(b) X-axis

(c) (0, 1)

(d) (1, 0)

Answer: (b) X-axis

(a) III

(b) II

(c) IV

(d) I

Answer: (d) I

(a) (-3, 9)

(b) (9, 3)

(c) (3, 9)

(d) (3, -9)

Answer: (d) (3, -9)

(a) I Quadrant

(b) II Quadrant

(c) III Quadrant

(d) IV Quadrant

Answer: (a) I Quadrant

**Q4: For a point, if the abscissa is -3 and the ordinate is 5, then it lies in the ___ quadrant.**(a) I

(b) II

(c) III

(d) IV

Answer: (b) II

**Q5: The coordinates of any point on the Y-axis are of the form (0, b), where |b| is the distance of the point from the ____.**(a) Y-axis

(b) X-axis

(c) (0, 1)

(d) (1, 0)

Answer: (b) X-axis

**Q6: For x = 3, y = 2, u = -9, v = 13 the point (x + y, u + v) lies in the ___ quadrant.**(a) III

(b) II

(c) IV

(d) I

Answer: (d) I

**Q7: Mirror Image of point (3, 9) on x-axis is:**(a) (-3, 9)

(b) (9, 3)

(c) (3, 9)

(d) (3, -9)

Answer: (d) (3, -9)

**Q8: A point both of its coordinates are positive will be in:**(a) I Quadrant

(b) II Quadrant

(c) III Quadrant

(d) IV Quadrant

Answer: (a) I Quadrant

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