Lesson Notes By Weeks and Term v4 - SHS 1

Lesson Video

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Performance objectives

• Define and explain the shortest distance between a point and a line.
• Calculate the perpendicular distance from a point to a line using a formula.
• Derive the equation of a line and use it to find the perpendicular distance.
• Determine the distance between two parallel lines.
• Apply these concepts to real-life situations.

Lesson summary

This lesson introduces the concept of finding the shortest distance from a point to a straight line. In our daily lives, we are always looking for the most efficient route – the shortest path to walk, the quickest way to connect a pipe, or the most direct line for a boundary. In coordinate geometry, this "shortest path" has a precise mathematical meaning: it is the perpendicular distance. We will explore this idea intuitively, derive a powerful formula to calculate it, and apply it to solve practical problems relevant to our Ghanaian context, from land surveying in our communities to planning infrastructure.

Lesson notes

Part 1: The Concept of "Shortest Distance"

Imagine you are standing at a point 'P' in a large, open field next to a long, straight road, 'L'. You want to walk to the road. You could walk in many different directions to reach the road. Question for thought: Which path is the shortest? Discovery: If you walk straight towards the road such that your path makes a right angle (90°) with the road, that will be the shortest possible distance. Any other path that is slanting will be longer because it becomes the hypotenuse of a right-angled triangle, and the hypotenuse is always the longest side.

Key Principle: The shortest distance from a point to a line is the length of the perpendicular line segment from the point to the line. Part 2: The Formula for Perpendicular Distance

While we can understand the concept intuitively, we need a precise way to calculate this distance using coordinates.

Evaluation guide

• Deduce the shortest distance between a point and a line and use the knowledge of
• intercepts and right -angled triangles to find the perpendicular distance from an external
• point to a line.
• shortest distance between two lines. Real -life activities to measure these distances in the classroom