Thursday, July 5, 2012

Class 9 - Maths - Coodinate Geometry

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.
Answer:  A(2, 4), B(0, -3), C(-3, -5) and D(5, 0)


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)

Answer:  (d) (-5, 0)

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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