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
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and
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or
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and
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