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Key Formulas
Distance in the Coordinate Plane
Distance = 
, if you’re measuring
the distance between the points (x1,y1)
and (x2,y2).
, if you’re measuring
the distance between the points (x1,y1)
and (x2,y2).Midpoint Between Two Points
Midpoint = (
, 
), where the endpoints of a line
segment are (x1, y1)
and (x2, y2).
, ), 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.
Slope-Intercept Form of the Equation of a 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 of a Line
Slope = 
, where two points
on the line are (x1, y1)
and (x2, y2).
, where two points
on the line are (x1, y1)
and (x2, y2).Standard Form of the Equation of a Circle
(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.
Standard Form of the Equation of an Ellipse
= 1, where the
ellipse is centered at (h, k)
and has a horizontal axis of length 2a and a vertical axis of length
2b.Standard Form of the Equation of a Parabola
y = a(x – h)2 + k,
where a, h, and k are
constants.
Standard Form of the Equation of a Hyperbola
– 
= 1, where a, b, h,
and k are constants. When centered at the origin,
the equation simplifies to 
– 
= 1.|
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