2. RENÉ DESCARTES
• Who was he?
• What is he known for?
• How is he related to our topic
3. CARTESIAN SYSTEM
• A Cartesian coordinate system is a coordinate system that specifies each point
uniquely in a plane by a pair of numerical coordinates, which are the signed
distances to the point from two fixed perpendicular directed lines, measured in the
same unit of length.
• One can use the same principle to specify the position of any point in three-
dimensional space by three Cartesian coordinates, its signed distances to three
mutually perpendicular planes (or, equivalently, by its perpendicular projection onto
three mutually perpendicular lines). In general, n Cartesian coordinates (an element
of real n-space) specify the point in an n-dimensional Euclidean space for any
dimension n. These coordinates are equal, up to sign, to distances from the point to
n mutually perpendicular hyperplanes.
4. • Cartesian coordinates are the foundation of analytic geometry, and provide
enlightening geometric interpretations for many other branches of
mathematics, such as linear algebra, complex analysis, differential geometry,
multivariate calculus, group theory and more. A familiar example is the
concept of the graph of a function. Cartesian coordinates are also essential
tools for most applied disciplines that deal with geometry, including
astronomy, physics, engineering and many more. They are the most common
coordinate system used in computer graphics, computer-aided geometric
design and other geometry-related data processing
7. • The position of any point on the Cartesian plane is described by using two
numbers, (x, y), that are called coordinates. The first number, x, is the
horizontal position of the point from the origin. It is called the x-coordinate.
The second number, y, is the vertical position of the point from the origin. It
is called the y-coordinate. Since a specific order is used to represent the
coordinates, they are called ordered pairs.
• Cartesian plane with the point P(x, y) marked
• For example, an ordered pair (4, 5) represents a point 4 units to the right of
the origin in the direction of the x-axis, and 5 units above the origin in the
direction of the y-axis as shown in the diagram below.
8. • We say that:
• The x-coordinate of point P is 4; and the y-coordinate of point P is 5.
• Or simply, we can say that:
• The coordinates of point P are (4, 5).
•
Note the following:
• For the point P(4, 5), the ordered pair is (4, 5). So:
4 is the x-coordinate, and
5 is the y-coordinate.
• P(4, 5) means P is 4 units to the right of and 5 units above the origin.
9. LETS SEE WHAT YOU HAVE LEARNT
• There will be 4 teams
• The 1st row, the 2nd row, 3rd row and the 4th row.
• The on our right will be the 1st row.
• There are 2 marks to a right answer and -1 for a wrong answer
• You can pass the questions if you don’t know the answer.
• You get 1 mark for passed question but no negative.
• The first answer heard by us will be called the final answer
• If a member of another team prompts an answer they will be reset to 0
• There will be 4 questions for each row.
• 10 seconds will be give for Q1 – 4, 15 seconds for Q5 – 8, 20 seconds for Q9 - 16
10. • Q1 – Goes to Row 1
• Q- In which quadrant lies the point (3,2) lie?
• A) I
• B) II
• C) III
• D) IV
• A) I
11. • Q2 – Goes to Row 2
• Q- The point (5,-2) and (-2,-5) lie in the:
• A) same quadrants
• B) II and III quadrants respectively
• C) II and IV quadrants respectively
• D) IV and III quadrants respectively
• D) IV and III quadrants respectively
12. • Q3 – Goes to Row 3
• Q- The point of intersection of X and Y axes is called
• A) Null Point
• B) Common Point
• C) Origin
• D) None of These
• C) Origin
13. • Q4 – Goes to Row 4
• Q- A point both of whose coordinates are positive lies in
• A) I
• B) II
• C) III
• D) IV
• A) I qudrant
14. • Q5 – Goes to Row 1
• Q- Points (1,-1), (2,-2), (4,-5) and (-3,-4)
• A) lies in II quadrant
• B) lies in III quadrant
• C) lies in IV quadrant
• D) do not lie in same quadrant
• D) do not lie in same quadrant
15. • Q6 – Goes to Row 2
• Q- The point (0,10) lies on:
• A) +ve x-axis
• B) –ve x-axis
• C) +ve y-axis
• D) –ve y-axis
• C) +ve y-axis
16. • Q7 – Goes to Row 3
• Q- The point (2,3) is at a distance of __________ units from x-axis
• A) 2 units
• B) 5 units
• C) 3 units
• D) None of these
• C) 3 units
17. • Q8 – Goes to Row 4
• Q- The coordinates of the point which lies on y-axis at a distance of 4 units in the
negative direction of y-axis is
• A) (0,4)
• B) (4,0)
• C) (0,-4)
• D) (-4,0)
• C) (0,-4)
• Since it lies on the y-axis , x-coordinate is 0
18. • Q9 – Goes to Row 1
• Q- The distance of a point (0.-3) from the origin is:
• A) 2 units
• B) -3 units
• C) can’t be determined
• D) 3 units
• D) 3 units
• As the distance can never be negative only direction can be
19. • Q10 – Goes to Row 2
• Q- The perpendicular bisector of a line segment AB passes through the origin. I he
coordinates of A are (-2,0), the coordinates of b are.
• A) (2,2)
• B) (-2,2)
• C) (0,2)
• D) (-4,0)
• A) 0,2
20. • Q11 – Goes to Row 3
• Q- Which of the following points are collinear
• A) P(0,5), Q(5,0), R(-5,0)
• B) A(3,4), B(0,-7), C(0,8)
• C) X(6,0), Y(-10,0) , Z(0,0)
• D) L(-1,3), M(-3,-4), N(3,4)
• C) X(6,0), Y(-10,0) , Z(0,0)
• As all the points lie on the x axis they are collinear
21. • Q12 – Goes to Row 4
• Q- An ant moves 3 units along x-axis from origin and hence reaches at point P, the
moves 4 units from P along y-axis and reaches point Q. What are the coordinates of
points P and Q?
• A) (0,3) ; (3,4)
• B) (0,3) ; (4,3)
• C) (3,0) ; (3,4)
• D) (3,0) ; (4,3)
• C) (3,0) ; (3,4)
22. • Q13 – Goes to Row 1
• Q- A point is at a distance of 3 units from the x-axis and 5 units from the y-axis. Which
of the following ma be the coordinates of the point.
• A) (5,-3)
• B) (-5,3)
• C) (-5,-3)
• D) all of the above
• D) all of the above
• Since the direction is not mentioned all the given points are possible
23. • Q14 – Goes to Row 2
• Q- Ordinate of all points on the x-axis is:
• A) 0
• B) 1
• C) -1
• D) Any number
• A) 0
• Ordinates are y-axis
• All the points on x-axis will have zero coordinates.
24. • Q15 – Goes to Row 3
• Q- For x=3, y=2, u=-9, v=13, the point [(x+y), (u-v)] lies in which quadrant?
• A) III
• B) II
• C) IV
• D) I
• C) IV
• As the coordinates are 3+2 , -9-13 = 5,-22 so IV quadant
25. • Q16 – Goes to Row 4
• Q- Mirror image of point (3,9) along x-axis is
• A) (-3.,9)
• B) (9,3)
• C) (3,9)
• D) (3,-9)
• D) (3,-9)
• To find the mirror image along the x-axis, change the sign of y-coordinate
26. • A Presentation By –
• Khush Ramani
• Explanations By –
• Anish
• Jay Pandit
• Aiyush Dwivedi
• Quiz Conducted By –
• Rudransh Gupta
• Sources –
• Google
• Wikipedia
• Mathslearning.com
