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Understanding Coordinate Geometry: Distance and Section Formula in Mathematics

This lesson plan for Class 10 Mathematics, covering the period from December 1st to 15th, 2013, focuses on introducing students to the concepts of coordinate geometry. The aim is to cultivate interest in the subject while emphasizing the practical applications of the distance and section formulas. By utilizing geometric representations and Pythagorean theorem, students will learn to calculate distances between points in a plane. Assignments will include exercises for practice and deeper understanding of these foundational concepts.

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Understanding Coordinate Geometry: Distance and Section Formula in Mathematics

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  1. Lesson PlanFrom 1st dec. to 15th dec. 2013 Class 10 – A Subject: MathematicsNo. of periods in a week: 7Topics: Coordinate geometry Aim: To create interest in the subjectSpecific Aim:To make the students understand the need of coordinate geometryTomake the students understand the concept of distance formula and section formula and to apply the same in finding the distance between two points in a plane.

  2. Distance formula Suppose we want to find the distance between two cities without actually measuring them, we can graphically represent it as shown in the figure, We can use Pythagoras theorem to find the distance Y 15km X 36 km

  3. Now suppose we have two points on the x axis and y axis as shown in the figure The distance from B to A =6-4=2 The distance from D to C = 6-3 = 3 D 6 5 4 3 2 1 Here also we can apply the Pythagoras theorem to find the distance AC and BD C A B 0 1 2 3 4 5 6 7 8 9 10

  4. Q (8,6) 8 7 6 5 4 3 2 1 PQ2 = PT2 +QT2 (x2 – x 1)2 + (y2 - y 1)2 P (4,6 This is known as distance formula 1 2 3 4 5 6 7 8 9 10 11 12

  5. Q (x2,y2 8 7 6 5 4 3 2 1 Suppose we have a situation In which line AQ is divided in the ratio of m1 and m2 P (x,y) C x1, y1 B A R 1 2 3 4 5 6 7 8 9 10 11 12

  6. In ∆PAB~ PQC PA = AB = PB QP PC QC x -x1= y –y1 = m1 x2 –x y2 –y m2 Hence we can find the value of x and y x= m 1x 2+m 2x1 m 1+m2 y= m 1 y2 + m 2y1 m 1+m2

  7. A • Similarly the area of the triangle can be found by using distance formula C B Q P R Area of a triangle ABC = Area of trapezium ABQP + Area of trapezium APRC- Area of trapezium BQRC

  8. Summary In this chapter we have dealt with the following • The distance formula • The section formula • Area of triangle using distance formula.

  9. Assignment Exercise 7.1 and 7.2 will be given and some extra questions will be given as worksheet.

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