Coordinate Plane
In short: The coordinate plane is a flat grid where two number lines, one sideways and one upright, cross at 0 so that each point can be named by a pair (x, y).
6th GradeGeometry6.NS.C.6b
What is Coordinate Plane?
Picture a city map with perfectly straight streets: that is a coordinate plane. One number says how far to go sideways, a second says how far to go up or down, and together they pin down exactly one location.
Precisely, two perpendicular number lines meet at the origin \((0, 0)\), the horizontal x-axis and the vertical y-axis. They cut the surface into four quadrants and give every point its own ordered pair \((x, y)\).
How to spot it
- A map uses numbered blocks east-west and north-south, and a place is given by two numbers.
- A problem asks you to plot points or draw a polygon from a list of pairs.
- You need to find the distance between two points that share a row or a column.
- A graph shows axes with arrows and labels, and the points use positive and negative values.
The method
- Start at the origin \((0, 0)\) where the two axes cross.
- Travel sideways by the first number: right when it is positive, left when it is negative.
- From there move parallel to the y-axis by the second number: up if positive, down if negative.
- Mark the point and label it with its pair, such as \(A(3, 2)\).
Coordinate Plane: solved example
Problem
On a city map drawn as a coordinate plane, the library is at \((-3, 4)\) and the bakery is at \((2, 4)\), each unit being one block. How many blocks apart are they?
Solution
Both points have y-coordinate 4, so they lie on the same horizontal street.
Count the gap along the x-values: \(2 – (-3) = 5\). The library and the bakery are 5 blocks apart.
Try it
Question 1
A skateboarder leaves the origin, rolls 6 units west and then 2 units north. What is the stopping point?
Show the answer
Left is negative x and up is positive y, so you stop at \((-6, 2)\).
Question 2
The points \((4, -1)\) and \((4, -8)\) are corners of a fence. How long is that side?
Show the answer
The x-values match, so count along y: \(|-1 – (-8)| = 7\) units.
Coordinate Plane vs. Ordered Pair
The plane is the whole grid, the surface with its two axes. An ordered pair is a single address on that grid, two numbers in a set order. The plane holds infinitely many pairs, and swapping the order, \((3, 2)\) versus \((2, 3)\), lands on a different point.
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Whole dictionary: A–Z · 6th Grade · Geometry