United University

Geometry Grade 9. Coordinate method on a plane. Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 16 hours

This interactive course introduces 9th-grade students to the coordinate method in geometry. It offers a structured exploration of essential topics such as the coordinate plane, trigonometric ratios and identities, midpoint and distance formulas, equations of a circle, and equations of a straight line. Through interactive problem-solving and practice exercises, students will strengthen their understanding of geometric relationships and analytical geometry.

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This interactive course introduces 9th-grade students to the coordinate method in geometry. It offers a structured exploration of essential topics such as the coordinate plane, trigonometric ratios and identities, midpoint and distance formulas, equations of a circle, and equations of a straight line. Through interactive problem-solving and practice exercises, students will strengthen their understanding of geometric relationships and analytical geometry.

Key Features of the Course

  • Interactive learning through problem-solving tasks and exercises
  • Development of analytical and spatial reasoning skills
  • Aligned with national curriculum standards in mathematics
  • Engaging review tasks and independent assignments for consolidation

Course Modules

Module 1: Coordinate Method on a Plane

  • Introduction
  • Welcome message to 9th-grade students
  • Lesson 1: The Coordinate Plane
  • Solve problems and complete exercises
  • Solve problems and complete exercises
  • Lesson 2: Sine, Cosine, Tangent of Angles from 0° to 180°. Trigonometric Identities
  • Solve problems and complete exercises
  • Solve problems and complete exercises
  • Lesson 3: Midpoint Coordinates. Distance Between Two Points with Given Coordinates
  • Solve problems and complete exercises
  • Solve problems and complete exercises
  • Lesson 4: Equation of a Circle
  • Solve problems and complete exercises
  • Solve problems and complete exercises
  • Lesson 5: Equation of a Line
  • Solve problems and complete exercises
  • Solve problems and complete exercises
  • Independent Homework #1
  • Solve the tasks
  • Review Exercises for Section 1
  • For § 1
  • For § 2
  • For § 3
  • For § 4
  • For § 5
  • Summary of Section 1

Expected Learning Outcomes

  • Gives examples of relationships mentioned in the content
  • Explains:
    • what sine, cosine, and tangent of angles from 0° to 180° are; what an equation of a figure is
    • how to define a line and a circle on the coordinate plane
  • Formulates theorems about:
    • distance between two points; midpoint coordinates of a segment
  • Writes and explains:
    • formulas for midpoint coordinates and distance between two points
    • equations of a circle and a straight line
  • Illustrates and identifies geometric figures (line, circle) on a diagram using their equations in a given coordinate system
  • Calculates:
    • midpoint coordinates of a segment
    • distance between two points with given coordinates
  • Proves theorems about:
    • distance between two points; midpoint coordinates of a segment
  • Applies studied formulas and equations of figures to solve problems

This course builds strong geometric fundamentals and analytical skills by integrating theoretical knowledge with real-world problem-solving. Students will explore geometry through a logical, coordinate-based approach, enhancing both academic performance and mathematical thinking.

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