Bab 7 (Part 1) Matematik Tambahan Tingkatan 4 KSSM 7.1 Pembahagi Tembereng Garis

Introduction

This tutorial covers the topic of "Pembahagi Tembereng Garis" (Segment Division of Lines) as part of the KSSM mathematics curriculum for Form 4 students. It aims to provide a clear understanding of how to effectively divide a line segment and apply geometric concepts in coordinate geometry.

Step 1: Understanding Pembahagi Tembereng Garis

• Definition: Pembahagi Tembereng Garis refers to the concept of dividing a line segment into specific ratios.
• Importance: This concept is essential for solving problems related to geometry and coordinate systems.

Key Concepts

• Ratio: A ratio indicates how much one quantity is compared to another. For example, dividing a line segment in the ratio 2:3 means that the segment is split into five equal parts, where two parts go to one section and three parts to another.
• Coordinates: When dividing a line segment, understanding the coordinates of the endpoints is crucial.

Step 2: Determining Coordinates for Division

• Identify Endpoints: Determine the coordinates of the endpoints of the line segment, say A(x1, y1) and B(x2, y2).
• Ratio Definition: Define the ratio in which the segment is to be divided. For instance, if you want to divide the segment in the ratio m:n, you will use these values in the calculations.

Formula for Finding the Division Point

To find the coordinates of the point P that divides the line segment AB in the ratio m:n, use the following formulas:

• ( P_x = \frac{mx_2 + nx_1}{m + n} )
• ( P_y = \frac{my_2 + ny_1}{m + n} )

Example

• Let A(2, 3) and B(8, 9) be your endpoints, and you want to divide it in the ratio 1:2.
  • ( P_x = \frac{1 \cdot 8 + 2 \cdot 2}{1 + 2} = \frac{8 + 4}{3} = 4 )
  • ( P_y = \frac{1 \cdot 9 + 2 \cdot 3}{1 + 2} = \frac{9 + 6}{3} = 5 )
• Therefore, the point P is (4, 5).

Step 3: Practical Applications

• Geometric Problems: Use this method to solve various geometric problems, such as finding midpoints or centroids of shapes.
• Real-World Scenarios: This technique can also be applied in real-world situations, such as in architecture or engineering, where precise measurements are required.

Conclusion

In this tutorial, we explored the concept of Pembahagi Tembereng Garis, learned how to determine the coordinates for dividing a line segment using ratios, and discussed its applications. Understanding how to divide segments accurately is crucial for further studies in geometry and mathematics. For the next steps, practice solving additional problems involving segment division and explore how these principles apply in different geometric contexts.