Algebra Fundamentals
Coordinate Geometry
Measure how far apart points are on the coordinate plane: separations across and up, distances you can estimate and compare, areas of rectangles, triangles and polygons, coordinates written with letters, Pythagoras' theorem built from squares, and the equations of circles.
THE SYLLABUS
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Separation Between Points
Every point has coordinates (x, y). Between two points, the horizontal separation is the difference of their x-coordinates and the vertical separation is the difference of their y-coordinates.
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Combining Separations
A point that is separated both horizontally and vertically from another is farther away than a point with just one of those separations: the distance is at least as large as each separation.
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The Closest Point
To find the closest point, compare separations: with the same horizontal separation the least vertical separation is closest, and increasing either separation always increases the distance.
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Comparing Distances
The straight line between two points is never longer than the sum of their horizontal and vertical separations, and it is shorter whenever both separations are there, so a diagonal point can be closer than a point straight across.
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Level Check
Fifteen questions with no hints on measuring separation: the farthest and the closest of four points on grids of every size, distances along one line typed as the difference of two coordinates, and a walk in two legs.
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