SAT Math: Use the distance formula and midpoint formula in the coordinate plane
22+ practice questions in Praczo
The concept, explained
- 1
Distance between (x₁, y₁) and (x₂, y₂): d = √((x₂ − x₁)² + (y₂ − y₁)²). This is just the Pythagorean theorem applied to coordinates.
- 2
Midpoint: ((x₁ + x₂)/2, (y₁ + y₂)/2). Simply average the x-coordinates and the y-coordinates.
- 3
Check: the midpoint should lie halfway between the two points — if it's not visually between them on a sketch, you've made an error.
- 4
For 3D coordinates, extend the formulas: include a z-term under the square root for distance, and average the z-values for midpoint.
- ✗ Subtracting coordinates in inconsistent order — both (x₂ − x₁) and (y₂ − y₁) must use the same "point 1" reference, though squaring removes sign issues.
- ✗ Forgetting to take the square root when computing distance.
SAT-style practice
What is the distance between the points (1, 2) and (4, 6)?
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