It is required to consutrct the equations of the three road centerlines AB, CD,

Question

It is required to consutrct the equations of the three road centerlines AB, CD, and EF, where lines AB and CD are parallel lines and lines AB and EF are perpendicular to each other. Points A, B, C, and E were observed using GPS in the Florida West State Plane Coordinate System and found to be as follows:

It is required to construct the equations of the three road centerlines AB, CD, and EF, where lines AB and CD are parallel lines and lines AB and EF are perpendicular to each other. Points A, B, C, and E were observed using GPS in the Florida West State Plane Coordinate System and found to be as follows: A (E= 5152270.62 N-1351454.24), B (E=5155453.95 N=1353731.41), C (E=5153574.16 N=1352986.65), E (E=5151736.56 N=1353385.45) Write the general equations of all 3 lines.

Explanation / Answer

equation of AB
y-y1 ={y2-y1}/{x2-x1} [x-x1]
y-1351454.24= [1353731.41-1351454.24 /5155453.95 -5155270.62] * x-5155270.62
y-1351454.24= 12.42*(x-5155270.62)
y=12.42x -6.2677*107

equation of CD
slope will be same as 12.42
y- 1352986.65=12.42{x-5153574.16}
y =12.42x - 6.26544*107

equation of EF
perpendicular to AB
slope will be=-1/12.42=-0.0805

y-1353385.45= -0.0805{x-5151736.56}

y= 1.7681*106 - 0.0805x

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