Lesson Notes By Weeks and Term v4 - SHS 1
PATTERNS AND RELATIONS
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PATTERNS AND RELATIONS
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Subject: Mathematics
Class: SHS 1
Term: 1st Term
Week: 17
Grade code: 1.2.2.LI.2
Strand code: 2
Sub-strand code: 2
Content standard code: 1.2.2.CS.21
Indicator code: 1.2.2.LI.2
Theme: ALGEBRAIC REASONING
Subtheme: PATTERNS AND RELATIONS
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This lesson explores the fundamental properties of straight lines on the Cartesian plane. We see straight lines everywhere in our lives—in the design of our buildings in Accra, the layout of farms in the Volta Region, and the patterns in Kente cloth. By understanding the mathematics behind these lines, we can describe their length, their steepness, and their relationship to other lines. This knowledge is crucial for fields like engineering, architecture, surveying, and even computer graphics. Today, we will learn how to calculate the distance between any two points and how to determine if lines are parallel (like railway tracks) or perpendicular (like the corner of a room).
Part A: The Cartesian Plane and Coordinates The Cartesian plane (or x-y plane) is a grid system we use to locate points. Each point has a unique address called coordinates (x, y). The first number (x) tells us how far to move horizontally (left or right) from the origin (0,0), and the second number (y) tells us how far to move vertically (up or down). Part B: The Distance Between Two Points The distance between two points is simply the length of the straight line segment connecting them. We can find this length using a formula derived from the Pythagoras Theorem.
Imagine two points, P(x₁, y₁) and Q(x₂, y₂).
The horizontal change (run) is `Δx = x₂ - x₁`. The vertical change (rise) is `Δy = y₂ - y₁`. These two changes form the legs of a right-angled triangle, and the distance `d` between P and Q is the hypotenuse.
By Pythagoras' Theorem, `d² = (Δx)² + (Δy)²`. Therefore, the distance formula is: d = √[(x₂ - x₁)² + (y₂ - y₁)²]