Ranjit plotted two points in the Cartesian plane and joined them by using a straight line. He found that this straight line cuts the Y.Axis . Which of these could be the pair of points that he plotted.
OPTIONS
a) (-6-6) and (-6,6)
b) (5.5) and (5.-5)
c) (4-4) and (-4,-4)
d) (-3.4) and (-3,-4)
Answers
Answer:
Fluency with the arithmetic of the rational numbers
Knowledge of ratios
Congruent and similar triangles
Basic algebraic notation
Fluency with algebraic expressions and equations
Basic plotting points in the Cartesian plane including plotting points from a table of values.
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MOTIVATION
Coordinate geometry is one of the most important and exciting ideas of mathematics. In particular it is central to the mathematics students meet at school. It provides a connection between algebra and geometry through graphs of lines and curves. This enables geometric problems to be solved algebraically and provides geometric insights into algebra.
The invention of calculus was an extremely important development in mathematics that enabled mathematicians and physicists to model the real world in ways that was previously impossible. It brought together nearly all of algebra and geometry using the coordinate plane. The invention of calculus depended on the development of coordinate geometry.
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CONTENT
It is expected that students have met plotting points on the plane and have plotted points from tables of values of both linear and non linear functions.
The number plane (Cartesian plane) is divided into four quadrants by two perpendicular axes called the x-axis (horizontal line) and the y-axis (vertical line). These axes intersect at a point called the origin. The position of any point in the plane can be represented by an ordered pair of numbers (x, y). These ordered pairs are called the coordinates of the point.
The point with coordinates (4, 2) has been plotted on the Cartesian plane shown. The coordinates of the origin are (0, 0).
Once the coordinates of two points are known the distance between the two points and midpoint of the interval joining the points can be found.
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DISTANCE BETWEEN TWO POINTS
Distances are always positive, or zero if the points coincide. The distance from A to B is the same as the distance from B to A. We first find the distance between two points that are either vertically or horizontally aligned.
EXAMPLE
Find the distance between the following pairs of points.
a A(1, 2) and B(4, 2)b A(1, −2) and B(1, 3)
SOLUTION
a The distance AB = 4 − 1 = 3
Note: The distance AB is obtained from
the difference of the x-coordinates of
the two points.
b The distance AB = 3 − (−2) = 5
Note: The distance AB is obtained from
the difference of the y-coordinates of the
two points.