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Lesson Plan Math Class X (Ch-7) | Coordinate Geometry
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Board - CBSE |
CLASS –X |
SUBJECT- MATHEMATICS |
CHAPTER 7 : Coordinate Geometry |
- Concept and introduction of coordinate geometry.
- Graphs of linear equations and method of representing the ordered pairs on the graph.
- Distance formula and its applications in different problems.
- Section formula (internal division of the line), mid- point formula and the related problems.
- Area of triangle and method of proving that three points are collinear.
S No |
TOPIC [For Complete Explanation of the topic] |
1 |
Introduction of coordinate geometry Coordinate geometry is the combination of Algebra and Geometry. Before start this topic teacher will explain the Cartesian coordinate system. Here teacher will
explain Horizontal line, Vertical line, ordinate, abscissa, point on x-axis,
point on y-axis, origin, quadrant etc. |
2 |
Distance between two points Plot
two points on the graph and then derive the distance formula by applying the
Pythagoras theorem. Distance
between two points A(x_{1},y_{1}) and B(x_{2}, y_{2})
is given by \[d=|AB|=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\] |
3 |
Collinearity of three points by distance formula Explain
the concept of collinearity of three points by using the distance formula. Three
or more points are said to be collinear if all the points lie on the straight
line. In
order to prove that three points are collinear we shall prove the following
statement. If
A(x_{1}, y_{1}) , B(x_{2}, y_{2}) and C(x_{3},
y_{3}) are three points on the line then |AB| + |BC|
= |AC| |
4 |
Conditions for different types of quadrilateral With
the help of distance formula we can find the types of quadrilateral by using
the following concepts. Parallelograms: Opposite sides are equal but diagonals are not equal. Rectangle: Opposite sides are equal and diagonals are also equal. Rhombus: All sides are equal but diagonals are not equal. Square: All
sides are equal and diagonals are also equal. Teacher
will explain the concept by taking some examples. |
5 |
Now teacher will Explain
the problems related to the following statements. Any
point on the x-axis is (a, 0). Any
point of the y-axis is (0, b) Any point given equidistant from two given points. |
6 |
Section Formula Now
teacher will Explain the derivation of section formula and its implementation
in the different problems. If
A(x_{1},y_{1}) and B(x_{2}, y_{2}) are two
points on the straight line and if point P(x, y) divide the line
between A and B in m_{1} : m_{2}, then by section formula: \[P(x,y)=\left
(
\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}
\right )\] Teacher will also explain the implementation of this formula in different problems. Teacher may also provide some problems to the students. |
7 |
Mid Point Formula After this teacher will introduce the Mid-Point formula and give some problems to the students for practice. If
A(x_{1},y_{1}) and B(x_{2}, y_{2}) are two
points on the straight line and if point P(x, y) is the mid -
point of AB, then by Mid-Point formula \[P(x,y)=\left
(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} \right )\] |
8 |
Area of Triangle Now teacher will introduce the formula of finding the area of triangle and extend this formula to find the area of the quadrilateral. If
A(x_{1}, y_{1}) , B(x_{2}, y_{2}) and C(x_{3},
y_{3}) are three vertices of a triangle then area of triangle is
given by \[=\frac{1}{2}\left
[ x_{1}y_{2}+x_{2}y_{3}+x_{3}y_{1}-(y_{1}x_{2}+y_{2}x_{3}+y_{3}x_{1}) \right
]\] Explanation
of the formula This formula can also be used to find the area of quadrilateral
as follows \[=\frac{1}{2}\left
[
x_{1}y_{2}+x_{2}y_{3}+x_{3}y_{4}+x_{4}y_{1}-(y_{1}x_{2}+y_{2}x_{3}+y_{3}x_{1}+y_{4}x_{1})
\right ]\] |
9 |
Collinearity of three points by using area of triangle Three points are collinear if area of the triangle is equal to zero. Teacher will assign some problems to the students to apply this concepts. |
10 |
Centroid of Triangle Now teacher will give the knowledge of centroid of the triangle and suggest the formula used to find it. If A(x_{1}, y_{1}) , B(x_{2}, y_{2}) and C(x_{3}, y_{3}) are three vertices of a triangle then Centroid P(x,y) of triangle is given by \[P(x,y)=\left (
\frac{x_{1}+x_{2}+x_{3}}{3},\frac{y_{1}+y_{2}+y_{3}}{3} \right )\] |
- Learn the formulas of finding the distance between two points,
- Able to understand section formula and mid-point formula,
- Understand the formula of finding the area of triangle, quadrilateral and the centroid of the triangle.
- Know the implementation of all these formulas in different problems.
- Review questions and formulas given by the teacher.
- Students should make the presentation on the formulas and basic concepts of this chapter.
- Solve N.C.E.R.T. problems with examples.
- Solve assignment Multiple Choice Questions (MCQ) given by the teacher.
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ReplyDeleteVery helpful Sir 👍
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