14.1 Coordinates and distance · Unit 14 Position and transformation

1 · Teaching slidesuse ← → keys

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2 · Key words

coordinatesA pair of numbers (x, y) giving a position.

originThe point (0, 0), where the axes cross.

quadrantOne of the four regions the axes divide the plane into.

x-coordinateThe first number; how far across.

y-coordinateThe second number; how far up.

midpointThe point exactly halfway between two points.

axisOne of the two number lines, x across and y up.

3 · Summary of the sectionrevise from this

Coordinates are written (x, y) — across first, then up. (3, 1) and (1, 3) are different points.
The origin is (0, 0), where the axes cross.
The four quadrants are numbered anticlockwise from the top right: 1 (+, +), 2 (−, +), 3 (−, −), 4 (+, −).
A point on an axis is in no quadrant.
If two points share a y-coordinate the line is horizontal: subtract the x-coordinates.
If two points share an x-coordinate the line is vertical: subtract the y-coordinates.
A distance is never negative — take the size of the subtraction.
The midpoint of such a line is the average of the two coordinates.
None of this needs a grid; it is arithmetic on the coordinates.

PDFPrintable worksheet All 66 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons1 videos

Algebra Basics: Graphing On The Coordinate Plane

American mathantics

The four quadrants, and why coordinates are always written across first.

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Coordinates and distance