Today is rung 5 of 5 on this topic
Coordinate geometry
Can do: Uses distance, midpoint and slope to prove geometric properties algebraically.
Why it matters
It joins algebra and geometry into one system, which is the foundation of everything from calculus to computer graphics.
What it looks like when it's wobbly
Can calculate distance and slope but can't use them to prove a shape is what it claims to be.
⏱️ Two-minute check
"Given four points, prove the quadrilateral is a parallelogram."
Solid looks like: Uses slopes for parallel pairs, or midpoints of diagonals, and states the conclusion properly.
The full activity for this topic · 30 minutes
Prove the Shape
- 1Plot four points and guess the shape.
- 2List what would have to be true for that shape: which sides parallel, which equal, which angles.
- 3Calculate the slopes and distances needed and check each condition.
- 4Write the conclusion as a proper argument, not just a set of calculations.
- 5Then try to prove it's something stronger — a rhombus, a rectangle — and see if it holds.
If it's too hard
Verify a given shape's properties with the formulas.
If it's too easy
Prove three collinear points, or find an unknown coordinate that makes a property true.
Say this
"What would have to be true for it to be that shape? List the conditions, then test each one."