Midpoint_Formula_Grade8_Matatag_powerpoint

Midpoint formula

1. Midpoint Formula Grade 8 Mathematics – Matatag Curriculum Prepared by: [Your Name] Date: [Insert Date]

2. Learning Objectives At the end of the lesson, learners will be able to: • Plot points on the coordinate plane • Compute the midpoint of a line segment • Solve real-life problems involving midpoints

3. Review: Coordinate Plane • The coordinate plane is formed by the x-axis and y-axis. • A point is represented as (x, y). • The origin is (0, 0). • Quadrants I, II, III, and IV.

4. Connecting to Prior Learning Previously, you learned how to compute the distance between two points. Now we find the midpoint — the point halfway between two endpoints.

5. Midpoint Formula If A(x₁, y₁) and B(x₂, y₂) are two points, then the midpoint M is: M(xₘ, yₘ) = ((x₁ + x₂)/2 , (y₁ + y₂)/2)

6. Understanding the Formula • On the x-axis: midpoint’s x = average of x₁ and x₂ • On the y-axis: midpoint’s y = average of y₁ and y₂ • Midpoint lies halfway between endpoints.

7. Example 1 Find the midpoint of A(2, 3) and B(6, 7): xₘ = (2 + 6)/2 = 4 yₘ = (3 + 7)/2 = 5 Midpoint M(4, 5)

8. Example 2 Find the midpoint of C(-1, 4) and D(3, -2): xₘ = (-1 + 3)/2 = 1 yₘ = (4 + (-2))/2 = 1 Midpoint M(1, 1)

9. Practice Problems Find the midpoint of: 1. E(0, 0), F(4, 8) 2. G(-2, 5), H(2, 1) 3. I(7, -3), J(-1, 5)

10. Application A line segment joins P(-3, 2) and Q(5, 6). Find the midpoint. Bonus: If a point divides PQ in ratio 1:3, find its coordinates.

11. Common Mistakes • Forgetting to divide by 2 • Mixing up x’s and y’s • Sign errors Tip: Always plot points to verify!

12. Quick Quiz 1. Midpoint of (1, -2) and (7, 4) 2. If midpoint of AB is (5, 5) and A is (3, 1), find B. 3. True or False: Midpoint always lies in the same quadrant as endpoints.

13. Summary • Midpoint Formula: ((x₁ + x₂)/2 , (y₁ + y₂)/2) • Works for all points • Check by plotting! • Used in geometry and real-life contexts.

14. Assignment • Solve 5 midpoint problems. • Apply to real-life situation (e.g., midpoint between two places on a map). • Optional: Find a point dividing segment in other ratios.

15. References • DepEd Matatag Curriculum Guide – Grade 8 Mathematics • GeoGebra, Desmos tools • Textbook: Coordinate Geometry Basics