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M01.2 · Coordinates and a first look at vectors

A free, illustrated module of 4 lessons and one interactive in M01 Math Foundations: The coordinate plane; Right triangles and Pythagoras’ theorem; Distance, from the plane to many dimensions; Arrows: a first look at vectors.

M01.2 L0 · Foundation 4 lessons · about 100 min Live · in review

Part of M01 Math Foundations in the Mathematics track.

Two number lines crossed at right angles turn every point of a page into a pair of numbers, and every pair of numbers into a point. These four lessons build the coordinate plane, prove Pythagoras’ theorem, use it to measure the distance between two points in the plane, in space and in as many dimensions as a data table has columns, and then read the move from one point to another as an arrow: a first look at vectors.

What you need first. The number line, the order of operations, squares and square roots, and the expansion of (a + b) squared (M01.1). A little Python for the code sections: loops, functions, importing a module, lists and tuples (P01.3 to P01.6).

Lessons

1. The coordinate plane M01.2.1 25 min

   Two number lines crossed at right angles turn every point of a page into a pair of numbers. Learn to plot and read ordered pairs, find the change from one point to another and the midpoint between them, and turn a table of data into a scatter plot.

2. Right triangles and Pythagoras’ theorem M01.2.2 25 min

   Why is the straight line from (1, 2) to (4, 6) exactly 5 long? Measure angles in degrees, see why the angles of a triangle add up to 180 degrees, prove Pythagoras’ theorem by arranging four triangles in a square, and meet the two special triangles of trigonometry.

3. Distance, from the plane to many dimensions M01.2.3 25 min

   The two changes between two points are the legs of a right triangle, so Pythagoras gives the straight-line distance. Measure it in the plane, in space and for lists of any length, find a nearest neighbour by hand, and code it from scratch and with math.dist.

4. Arrows: a first look at vectors M01.2.4 25 min

   The move from one point to another is a list of changes, drawn as an arrow that may start anywhere. Write it as a bold letter and a column, find its length, see a point as the arrow from the origin, and add two moves by adding their changes.

The interactive

M01.2-X1 · Point and arrow explorer. Drag two points on a grid, or move them with sliders. The right triangle between them shows the horizontal and the vertical change, and the distance, the midpoint and the arrow from one point to the other update as numbers. It lives in Arrows: a first look at vectors.