Coordinate Geometry
Lessons in this chapter
About Coordinate Geometry
Coordinate Geometry extends 5th grade’s plane to all four quadrants, which is where the negative numbers from earlier in the year arrive on a graph.
Identify and Plot Points on the Coordinate Plane now includes negative coordinates, so the plane has four quadrants rather than one corner. The sign of each coordinate decides the quadrant: both positive is the first, negative x and positive y is the second, and so on anticlockwise.
Draw Polygons on the Coordinate Plane joins plotted points into shapes, which lets geometry be done with arithmetic. The side length of a rectangle with vertices at (−3, 2) and (4, 2) is the difference of the x-coordinates, so 7, and from there area and perimeter follow without any measuring.
This is the chapter where the two halves of 6th grade meet. The integer work supplies the negative coordinates, the algebra supplies the equations, and the plane is where an equation becomes a picture.
Both lessons here open as 6th grade math worksheets inside the page. Identify and Plot Points on the Coordinate Plane and Draw Polygons on the Coordinate Plane give practice questions worked one at a time and marked as you go, which is the fastest way to stop x and y being read in the wrong order. Free to try, with no login needed for your first 3.
Frequently asked questions
Identify and Plot Points on the Coordinate Plane extends the first quadrant children already know into all four, so coordinates can now be negative and the signs tell you which quadrant a point lands in. Draw Polygons on the Coordinate Plane then joins points into shapes and uses coordinates to find side lengths, which is the first time the grid does measuring rather than just locating. The chapter sits mainly in the Common Core domain Geometry (6.G), with the four-quadrant plotting itself belonging to The Number System (6.NS).
The four regions of the plane, numbered anticlockwise from the top right. In the first both coordinates are positive; in the second x is negative and y positive; in the third both are negative; in the fourth x is positive and y negative.
Go 3 left along the horizontal axis and 2 up. A negative x means left, a negative y means down.
Subtract the coordinates that differ. From (−3, 2) to (4, 2) the y-coordinates match, so the distance is 4 − (−3), which is 7.
Work out the side lengths from the coordinates, then use the usual area formula. No measuring is needed, which is the point of the chapter.
5th grade used only the first quadrant, with positive coordinates. This adds negatives and all four quadrants, and asks for polygons to be drawn.