Lesson Notes By Weeks and Term v4 - SHS 1
SPATIAL SENSE
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SPATIAL SENSE
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Subject: Additional Mathematics
Class: SHS 1
Term: 1st Term
Week: 20
Grade code: 1.2.1.LI.4
Strand code: 2
Sub-strand code: 1
Content standard code: 1.2.1.CS.1
Indicator code: 1.2.1.LI.4
Theme: GEOMETRIC REASONING AND MEASUREMENT
Subtheme: SPATIAL SENSE
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This lesson focuses on a fundamental concept in coordinate geometry: dividing a straight line segment into a specific ratio. In our daily lives, we often need to find points that are part way between two known locations. For instance, a town planner might need to place a new clinic one-third of the way along a straight road connecting two villages. A surveyor might need to place a boundary marker that divides a piece of land in a ratio of 2:3. By mastering the formulas for internal and external division, we gain powerful tools to solve such practical problems with precision.
This lesson will be broken down into three main parts: a) The concept of dividing a line segment. b) Internal Division of a line segment. c) External Division of a line segment. a) The Concept of Dividing a Line Segment
Imagine a straight sugar cane stick. If you have two points, A (one end) and B (the other end), dividing this stick means finding a point P on the stick. If you cut the stick at P, you get two pieces, AP and PB. The ratio of their lengths, AP:PB, is what we are interested in. Internal Division: The point P lies *between* A and B. It's like finding a spot on the road between Koforidua and Accra. External Division: The point P lies on the same straight line as A and B, but *outside* the segment AB. It's like continuing the road from Koforidua through Accra to a new location, still on the same straight path. b) Internal Division of a Line Segment
If a point `P(x, y)` divides the line segment joining the points `A(x₁, y₁)` and `B(x₂, y₂)` internally in the ratio `m:n`, then the coordinates of P are given by the formula:
P(x, y) = ( (mx₂ + nx₁) / (m + n) , (my₂ + ny₁) / (m + n) )