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Practice Set 5.2 Lecture 3 Co ordinate Geometry | SSC Class 10 Geometry| Maths 2 | Maharashtra Board

Yogesh Sir's Backbenchers・31 minutes read

The YouTube video series focuses on Coordinate Geometry, specifically discussing segment trisection and point calculations using section and midpoint formulas, emphasizing the ease of solving such problems despite repetitive nature. Various points such as A, B, P, Q, L, M, N, D, E, and F are calculated sequentially through formulas to divide segments into equal parts and determine coordinates efficiently.

Insights

  • Trisection of a line segment involves dividing it into three equal parts, requiring the use of the section formula and mid-point formula to find the coordinates of the trisection points.
  • The process of trisection becomes more complex as additional points are introduced, but the repetitive nature of calculations does not increase the difficulty level, emphasizing the importance of perseverance and systematic application of formulas for accurate solutions.

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Recent questions

  • How is trisection of a line segment achieved?

    By finding coordinates of trisection points using formulas.

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Summary

00:00

"Trisecting Line Segments: Easy Math Solutions"

  • The text introduces a YouTube video series on mathematics, specifically focusing on the geometry chapter named Coordinate Geometry.
  • The practice set 5.2 is being discussed, with lectures one and two already uploaded and lecture three planned for the day.
  • The completion status of questions from First to Ninth is mentioned, with today's focus on questions 10, 11, and 12.
  • The concept of trisection, dividing a line segment into three equal parts, is explained, emphasizing the need for two points to achieve this division.
  • The task at hand is to find the coordinates of the points that trisect the line segment, denoted as A and B, into three equal parts.
  • The process involves applying the section formula and mid-point formula to calculate the coordinates of the trisection points.
  • The coordinates of point P, dividing line segment A in a 1:2 ratio, are determined to be (0, 2) using the section formula.
  • The coordinates of point Q, the midpoint of line segment A, are calculated as (-2, -3) using both the section formula and mid-point formula.
  • The text emphasizes the ease of solving such problems by applying the section formula and mid-point formula, with the length of the solution increasing with the number of points involved.
  • It concludes by encouraging students not to be deterred by the length of the solution, as the repetitive nature of the calculations does not increase the difficulty level of the problem.

14:18

Trisection of Segment A: Calculations and Coordinates

  • Trisection of segment A into parts A, B, P, and Q is discussed.
  • Variables x1, y1, x2, and y2 are introduced for trisection calculations.
  • The value of A is determined as k + q b, with p k and q b being equal.
  • The ratio of A up pb7 to pub is found to be 1:2.
  • Point P divides segment A in the ratio 1:2, simplifying the process.
  • Coordinates of point P are calculated as 0, 2 using the section formula.
  • Point Q is identified as the midpoint of PB2, with coordinates -2, -3.
  • The final coordinates of the trisection points of segment A are determined as P(0, 2) and Q(-2, -3).
  • Segment A is divided into four equal parts using points A, L, M, and N.
  • The mid point formula is applied to find the coordinates of points L, M, and N, simplifying the solution process.

29:28

Calculating Points Using Section and Midpoint Formulas

  • Point D divides the line into two parts in a 2:3 ratio, allowing for the application of the section formula to calculate D accurately.
  • The midpoint C of AD can be determined using a formula, leading to the identification of point C.
  • By establishing D as the midpoint of C and E, point E can be calculated, followed by finding the midpoint F of E and B.
  • Applying the section formula on C reveals its coordinates, aiding in the subsequent identification of E and F through the midpoint formula.
  • The process involves finding points C, D, E, and F sequentially, utilizing the section and midpoint formulas for accurate calculations.
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