Math 150

Formulas

Steve Wilson

The proofs of these formulas can be found in the Analytic Foundations of Geometry.

1. The equation of the line that joins the points (x1, y1) and (x2, y2) is y = mx + b where m =

Once you know the slope, one can use the point-slope form of the equation to find the y intercept, but there are formulas.

2. The coordinates of the point where the lines

meet are

and

3. The foot of the point (x1, y1) in the line y = mx + b has coordinates

4. The distance from the point (x1, y1) to its foot in the line y = mx + b is

5. If (x1, y1) and (x2, y2) are two points on the line y = mx + b, then the distance between them is.

6. The coordinates of the points where the line y = mx + b meets the circle (x- x1)2 + (y - y1)2 = r2 are

and

or

and