Coordinate geometry

Practice 5 items →

Pythagoras on the plane. Students compute distance, midpoint, and a partition point, classify figures from their vertices, find polygon areas on the grid, and prove a quadrilateral is a parallelogram by slope and by distance.

Specification · for a parent or teacher
Part no.
coordinate-geometry
Course
High School Math 1 · Unit 15
Realm
Shapes
Difficulty
4 of 4 — Grade 7 / Math 1 core. Structure, models, proofs on the grid.
Qty
5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

compute distance, midpoint, and a point partitioning a segment in ratio m:nm:n; classify a triangle or quadrilateral from its vertices; find the area of a polygon on the grid.

Ready when

they prove a quadrilateral is a parallelogram two ways (distance, slope) from four vertices.

Formulas

Distance
d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
Midpoint
M=(x1+x22,y1+y22)M = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)

Watch for

midpoint as a sum not a mean; distance missing the square root.

Before · requires

After · used by

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coordinate-geometry

Items: coordinate-geometry-01 · coordinate-geometry-02 · coordinate-geometry-03 · coordinate-geometry-04 · coordinate-geometry-05