Key takeaway: The coordinate plane is a grid built from two perpendicular number lines, the x-axis and the y-axis, on which each point is pinned down by a pair of numbers.
Grade 66.NS.C.6bGeometry and Measurement
Definition of Coordinate Plane
A coordinate plane works like a city map where every address is two numbers. A horizontal number line (the x-axis) and a vertical one (the y-axis) cross at right angles at the origin, the point (0, 0).
The first number of an address says how far to walk east or west from the origin, and the second says how far to go north or south. Since the grid reaches in all four directions, negative values fit on it just as well as positive ones. People also call this flat surface the Cartesian plane, after the mathematician who proposed it.
Formula and notation
Points are labeled with a capital letter followed by the address:
\[A(x,\, y)\]
Here \(x\) is the horizontal position and \(y\) is the vertical position. For two points with the same \(y\)-value, the distance is \(|x_2 – x_1|\); with the same \(x\)-value, it is \(|y_2 – y_1|\).
Key facts
- The origin is where both numbers are zero, and the axes cross there.
- The axes divide the coordinate plane into four regions, called quadrants.
- Move horizontally first, then vertically, to find a point from its address.
- Points on an axis have a zero in one of their two numbers.
Coordinate Plane example
On a park map, the fountain is at \(A(-3,\, 4)\) and the playground is at \(B(5,\, 4)\). Each grid unit is 25 yards. How far apart are they?
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Both points have the same \(y\)-value, 4, so they lie on one horizontal line.
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Distance in units: \(|5 – (-3)| = 8\).
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Convert: \(8 \times 25 = 200\) yards.
The fountain and the playground are 200 yards apart.
Common mistake
Watch out
Lucas plots \((-2,\, 5)\) by going up 5 first and then right 2.
Why it is wrong
He went right instead of left. The first number, \(-2\), is the horizontal move, and the negative sign means left. Start at the origin, go 2 left, then 5 up.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Geometry and Measurement