2. Coordinate geometry
What are Coordinates?
Concept of coordinate.
Formulas for distance in coordinate geometry.
Formula for measuring.
Area of AABC, formed by the points A(x1 , y1), B(x2,y2), C(x3, y3)
is given by the numerical value of the expression.
AREA OF A TRIANGLE03
4. What is coordinate
A coordinate geometry is a branch of geometry where the position of the points
on the plane is defined with the help of an ordered pair of numbers also known
Understanding the Concept of Coordinates
•The point of intersection of the x and the y-axis is known
as the origin. At this point, both x and y are 0.
•The values on the right-hand side of the x-axis are
positive and the values on the left-hand side of the x-axis
•Similarly, on the y-axis, the values located above the
origin are positive and the values located below the origin
•When you have to locate a point on the plane, it is
determined by a set of two numbers. So, first, you have to
write about its location on the x-axis followed by its
location on the y-axis. Together, the two will determine a
single and unique position on the plane.
•Let X’OX and YOY’ be two perpendicular straight lines meeting at fixed point 0
then X’OX is called the x—axis and Y’OY is called the axis of y or y axis. Point
‘0’ is called the origin. x axis is known as abscissa and y—axis is known as
•The coordinate axes X’OX and Y’OY divide the plane into four parts called
quadrants, numbered I, II, III and IV anti-clockwise from OX.
•The coordinates of a point on the x-axis are of the form (x, 0), and of a point
on they— axis are of the from (0,y)
•The coordinates of a point on the x-axis are of the form (x, 0) and that of the point on the y-axis are (0, y).
9. The coordinates of the origin are (0, 0).
•10. The coordinates of a point are of the form (+ , +) in the first quadrant, (–, +) in the second quadrant, (–, –) in the
third quadrant and (+, –) in the fourth quadrant, where + denotes a positive real number and – denotes a negative real
•11. If x ≠ y, then (x, y) ≠ (y, x), and (x, y) = (y, x), if x = y.
•Since, distance is always non-negative (Positive), we take only the positive
7. •Area cannot be negative so, we shall ignore negative
sign if it occurs in a problem.
•To find the area of quadrilateral we shall divide it into
two triangles by joining two opposite vertices, find their
areas and add them.
•If the area of triangle is zero sq. units then the vertices
of triangle are collinear.
Area of AABC, formed by the points A(x1, y1),
B(x2,y2), C(x3, y3)
is given by the numerical value of the expression
AREA OF A TRIANGLE
8. CENIROID OF A TRIANGLE
If AD is a mediam of the triangle ABC and G
is its centroid, then AG/GD = 2/1.
The coordinates of the point G are
(x1 + x2 + x3 / 3 ,y1 + y2 + y3 / 3)
A(x1, y1), B(x2,y2), C(x3, y3)
The point where the medians of a triangle
meet is called the centroid of the triangle.
9. (I) Four points will form :
(a) a parallelogram if its opposite sides are equal, but diagonals are unequal.
(b) a rectangle if opposite sides are equal and two diagonals are also equal.
(c) a rhombus if all the four sides are equal, but diagonals unequal,
(d) a square if all sides are equal and diagonals are also equal
(II) Three points will form:
(a) an equilateral triangle if all the three sides are equal.
(b) an isosceles triangle if any two sides are equal.
(c) a right angled triangle if sum of square of any two sides is equal to square of the third side.
(d) a triangle if sum of any two sides (distances) is greater than the third side (distance).
(III) Three points A, B and C are collinear or lie on a line if one of the following holds
(i) AB + BC — AC
(ii) AC + CB AB
(iii) CA + AB CB.
10. Math is not the thing that you that you
It is the thing that you learn and use in your
whole life style.
Hope you like it
It is my pleaser to show you
-By Rahul Bera
BY Rahul Bera