MathGeometry & TrigonometryMedium frequency
SAT Math: Midpoint and Distance Formulas
20+ practice questions in Praczo
What you need to know
The concept, explained
- 1
Midpoint between (x₁,y₁) and (x₂,y₂): M = ((x₁+x₂)/2, (y₁+y₂)/2).
- 2
Distance: d = √((x₂−x₁)² + (y₂−y₁)²). This is the Pythagorean theorem applied to coordinates.
- 3
To find the other endpoint when given a midpoint and one endpoint, set up the midpoint formula and solve.
- 4
Distance formula gives the straight-line (hypotenuse) length between two points.
- 5
Vertical or horizontal distances are simpler: just subtract the coordinates that differ.
Common mistakes
- ✗ Averaging only the x-coordinates and forgetting the y-coordinate for the midpoint.
- ✗ Squaring the subtraction incorrectly: (x₂−x₁)² is not x₂²−x₁².
Try a sample question
SAT-style practice
What is the midpoint of the segment connecting (2, −5) and (8, 3)?
20+ questions ready to practice
Ready to master this concept?
Praczo tracks your mastery on all 179 SAT concepts — not just broad topics. One sample question is a start; drilling to mastery is how scores move.
3-day free trial — no credit card required