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
THE ONE THAT YOU HAVE DONE IS CORRECT.
<em>ALL</em><em> </em><em>DIAGONAL</em><em> </em><em>MATRICES</em><em> </em><em>ARE</em><em> </em><em>SQUARE</em><em> </em><em>MATRIX</em><em>.</em><em>.</em><em>.</em><em>.</em>
<em>HOPE</em><em> </em><em>TH</em><em>I</em><em>S</em><em> </em><em>HELP</em><em>S</em><em> </em><em>YOU</em><em>.</em><em>.</em><em>.</em><em>.</em><em>.</em><em>.</em><em>.</em>
F(5) = 21
look on the table and find where x=5 on the top row, the number that is with it is 21
f(x) = 7
x=6
look on the table and find where f(x)=7 on the bottom row, the number with it is 6
What is the least common denominator for fractions that have denominators of 5x+10 and 25x^2-100
Answer:
22.7%
Explanation:
Given that last year stock for company A was $7200
The stock for company B last year was worth $3510
Stock in company A decreased by 24%
This means the new value of stock for company A became;
(100-24)/100 *$7200
76/100*$7200
0.76*7200 =$5472
Stock in company B decreased by 20%
This means the new value of stock for company B became;
(100-20)/100 *$3510
80/100*$3510
0.8*$3510
$2808
Original investors stock value was = $7200+$3510 =$10710
New investors stock value is = $5472+$2808=$8280
Decrease in value of stock = $10710-$8280 =$2430
percentage decrease in stock value = decrease in stock/original value of stock *100%
=2430/10710 *100 =22.689
=22.7%
