Study guide: Use Coordinates and Shape Hierarchies
Plot ordered pairs, measure axis-aligned distances, interpret coordinate context, and organize figure categories.
Ideas to explain in your own words
- A coordinate plane combines perpendicular number lines.
- When two points have the same y-coordinate, their segment is horizontal and its length is the difference between x-coordinates.
- Coordinate axes can represent quantities other than directions on a room plan.
- A shape subcategory inherits all the attributes of its broader category.
Useful vocabulary
- ordered pair
- An x-coordinate followed by a y-coordinate.
- hierarchy
- An organization placing narrower categories within broader ones.
Watch your reasoning
- Coordinate order cannot generally be swapped.
- An endpoint coordinate is not a segment length unless the other endpoint is zero.
- A supplied point does not establish an unstated continuous trend.
- A true narrower-to-broader inclusion does not make its reverse true.
A worked review example
Plot (4,7): move four units right and seven up. The point (7,4) would be seven right and four up, so it is a different location. Both axes need equal intervals within their own labeled scale, and the ordered pair preserves their roles. Use x first and y second. Coordinate order cannot generally be swapped. Draw labeled perpendicular x and y axes with a marked origin.
Make a practice plan
- Plot Ordered Pairs from the Origin: Plot (3,8) and (8,3). Expected: distinct locations with reversed coordinate roles.
- Find Distance Along One Coordinate Direction: Points (6,2) and (6,11) have vertical distance 9 units.
- Interpret a Coordinate Pair in Its Stated Context: For x=days and y=pages, interpret (3,24). Expected: 24 pages at day three in the record.
- Organize Shape Families in a Hierarchy: Give a counterexample to every parallelogram is a rectangle. Expected: a non-right-angle parallelogram.