Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Proofs that use coordinates
Use slopes distances and midpoints to prove geometric claims
Problem types
- Decide what coordinates prove about a quadrilateral
Builds on
- Writing and critiquing a geometric proof
- Distance in the coordinate plane
- Slope of a line
- Proofs about parallelograms · Useful idea
Bisecting diagonals and congruent rectangle diagonals become coordinate tests: compare midpoints of diagonals and diagonal lengths.
- Proofs about triangles · Useful idea
The midsegment and median facts can be checked with coordinates: a midsegment has half the vector of the side it is parallel to.
- Side lengths from coordinates · Useful idea
Side lengths and vertices of a polygon on a grid are used to prove claims about its shape.
- Classifying quadrilaterals · Useful idea
Proving that a quadrilateral drawn on a grid is a rectangle or parallelogram uses its category definitions.
Leads to
- Slopes of parallel and perpendicular lines
- Dividing a segment in a given ratio · Extend the idea
Coordinate proofs use midpoints, and a point dividing a segment in a given ratio extends the midpoint.
Related skills
- Vectors and their components · Related idea
Vectors prove geometric claims in coordinates: a quadrilateral is a parallelogram when opposite side vectors are equal.
- What slides, flips, and turns keep the same · Shared foundations
- Average rate of change · Shared foundations
- Equations of circles · Shared foundations
- Theorems about circles · Shared foundations
Open the interactive map to explore lessons and skill connections.