presentation on co-ordinate geometery
- 1. For 10th class Explanation by Rahul Bera a math’s project
- 2. Coordinate geometry What are Coordinates? Concept of coordinate. Introduction01Content Plan Formulas for distance in coordinate geometry. Formula for measuring. DISTANCE FORMULA02 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
- 3. Basic knowledge to coordinate Geometry
- 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 as coordinates. 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 are negative. •Similarly, on the y-axis, the values located above the origin are positive and the values located below the origin are negative. •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.
- 5. Y -Y -X X I Quadrant III Quadrant II Quadrant IV Quadrant (+,+) (+,-)(-,-) (-,+) •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 ordinate. •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 number. •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 square root
- 6. DISTANCE FORMULA The distance between two points whose co-ordinates are P. (x1, y1) and Q (x2, y2).
- 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. Co-ordinate The coordinates of the point G are (x1 + x2 + x3 / 3 ,y1 + y2 + y3 / 3) G A(x1, y1), B(x2,y2), C(x3, y3) Co-ordinate numbers The point where the medians of a triangle meet is called the centroid of the triangle. Centroid A DB C ABCD X,Y G G 2
- 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 remember 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 my work Thank You -By Rahul Bera BY Rahul Bera Thank You