COORDINATE GEOMETRY (A) Main Concepts and Results
Cartesian system Coordinate axes Origin
Quadrants
Abscissa
Ordinate
Coordinates of a point Ordered pair
Plotting of points in the cartesian plane:
• In the Cartesian plane, the horizontal line is called the x-axis and the vertical line
is called the y-axis,
• The coordinate axes divide the plane into four parts called quadrants,
• The point of intersection of the axes is called the origin,
• Abscissa or the x-coordinate of a point is its distance from the y-axis and the ordinate or the y-coordinate is its distance from the x-axis,
• (x, y) are called the coordinates of the point whose abscissa is x and the ordinate is y,
• Coordinates of a point on the x-axis are of the form (x, 0) and that of the point on the y-axis is of the form (0, y),
CHAPTER 3
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COORDINATE GEOMETRY 25
• The coordinates of the origin are (0, 0),
• Signs of the coordinates of a point in the first quadrant are (+, +), in the second quadrant (–, +), in the third quadrant (–, –) and in the fourth quadrant (+, –).
(B) Multiple Choice Questions
Write the correct answer :
Sample Question 1: The points (other than origin) for which abscissa is equal to the ordinate will lie in
(A) I quadrant only (B) I and II quadrants
(C) I and III quadrants (D) II and IV quadrants Solution : Answer (C)
EXERCISE 3.1
Write the correct answer in each of the following : 1. Point (–3, 5) lies in the
(A) first quadrant (B) second quadrant
Answer:
ight
Step-by-step explanation:
Answer:
y=-1/5x+4/5
Step-by-step explanation:
9514 1404 393
Answer:
1,222,200
Step-by-step explanation:
A search using a computer program found ...
5432 × 225 = 1,222,200
__
1000 mod 225 = 100
4 × 225 = 900
This suggests that if we have some number of thousands whose digits total 9, that we will have the number of interest. Of course, we can add 200 to some number of thousands with a digit total of 7. The smallest such digit total will be had with the number 1222 using the specified digits {0, 1, 2}. This gives rise to the result above: 1222×1000 +200 = 1,222,200. It also explains why moving the 1 to the right will also give a multiple of 225.
