Coordinate GEO

August MS Wrap Up Topics:

Point (X,Y) to line (Ax+By+c=0) distance

([AX+BY+C])/(square root of a²+b²)

Point (x,y ) to Vert. (X=) Distance

[x-X]

Point (x,y) to Hori. (Y=) Distance

[y-Y]

Point (x,y) to Point (X,Y) Distance

square root of (X-x)² + (Y-y)²

Non Parallel Line to Line Distance

0 (they intersect)

Parallel Lines (Ax+By+C) & (AX+BY+C) Distance

([C-c])/ (square root of A²+B²)

What is the one rule for all point-to-line distance setups?

The line must be written in standard form in the correct order of Ax+By+C=0

What is the one rule for all parallel line-to-line distance setups?

Both lines must have equal Ax & By values (one must be scaled and/or reflected (-sign) to match the other if not equal)

Angle between two regular lines

Tan θ= [(m2-m1)/ (1+mm)], where m2 and m1 are the slopes of the two lines

Angle between two parallel lines

0 (parallel lines have equal slopes)

Angle between two perpendicular lines

90 (perpendicular lines have negative-reciprocal slopes)

Angle between Vert. line (X=) & line

θ= 90 - (Tan^-1 [M]), where m= slope of the non-vertical line

Angle between Hori. line (Y=) & Line

Tan θ= [M], where m= the slopes of the non-horizontal line