Coordinate geometry

Concept

The key tools when geometry meets coordinates:

Slope — m = (y₂ − y₁) / (x₂ − x₁)
Midpoint — M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Distance — d = √((Δx)² + (Δy)²)
Parallel lines have equal slopes; perpendicular lines have slopes that multiply to −1 (negative reciprocals).
Horizontal line y = k: slope 0. Vertical line x = h: slope undefined.
Equation of a circle centered at (h, k) with radius r: (x − h)² + (y − k)² = r²

Solution

Midpoint. Average the coordinates: ((1+7)/2, (3+11)/2) = (4, 7)

Distance. d = √((7−1)² + (11−3)²) = √(36 + 64) = √100 = 10

Midpoint (4, 7), distance 10.

Solution

Slope. Original slope is 3, so perpendicular slope is −1/3.

Point-slope. y − 5 = (−1/3)(x − 2)

Simplify. y = −x/3 + 2/3 + 5 = −x/3 + 17/3

y = −x/3 + 17/3.

8 questions on slope, midpoint, distance, parallel/perpendicular, and circle equations.

Practice test · 8 questions Question 1 of 8 · Score 0