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:
Step-by-step explanation:
Depending on the tools available to your 11y.o., it's a typical question for linear inequalities.
Where a,b,c are the # of 1,15,50 coins given by the buyer, and d,e,f the # of coins given back by the seller.
1×a + 15×b + 50×c > 1×d + 15×e + 50×f
a+b+c+1>=d+e+f
a+b+c >=2
Now, there are other clues in the text :
If the seller gives back money, then you didn't pay with 1's, otherwise, it means you overpay and you could have given fewer coins. So a=0.
Similarly, the seller cannot give you back a coin of 50, otherwise, you could have given fewer coins as the buyer. So f=0.
So that gives :
15×b + 50×c > 1×d + 15×e
b+c+1>=d+e
b+c >=2
From that point on, there is only a handful of scenarios to test.
The answer is 12.3 ft below sea level.
Because she is ascending (going up), 83.1 - 70.8 = 12.3 Ft
The volume of cone is 24
or 75.398 cubic centimeters, if the cone has a radius of 3 centimeters and height of 8 centimeters.
Step-by-step explanation:
The given is,
Formula for volume of cone, 
Where, B = 
Volume, 
From the given,
Radius, r = 3 centimeters
Height, h = 8 centimeters
volume, 
Volume of cone, V= 24 (volume in terms of )
( or )
Volume, V = (24 × 3.14 ) ( ∵ =3.14 )
V = 75.398 cubic inches
Result:
The volume of cone is 24 or 75.398 cubic centimeters, if the cone has a radius of 3 centimeters and height of 8 centimeters.
