Distance = if you’re measuring the distance between the points (x₁, y₁) and (x₂, y₂).

 

Distance = if you’re measuring the distance between the points (x₁, y₁, z₁) and (x₂, y₂, z₂).

 

Midpoint = (, ), where the endpoints of a line segment are (x₁, y₁) and (x₂, y₂).

    Point-Slope Form of the Equation of a Line

y – y₁ = m(x – x₁), where m is the slope of the line, and (x₁, y₁) is a point on the line.

 

y = mx + b, where m is the slope of the line, and b is the y-intercept of the line. Both m and b are constants.

 

Slope = , where two points on the line are (x₁, y₁) and (x₂, y₂).

 

(x – h)² + (y – k)² = r², where (h, k) is the center of the circle, and r is the radius. When centered at the origin, the equation simplifies to x² + y² = r².

 

y = a(x – h)² + k, where a, h, and k are constants.