Partitioning a parcel by a cut line of given direction
Three acres are to be severed from an eight-acre tract by a line parallel to the frontage. Set up the cut area as a quadratic in the perpendicular offset, solve it, and stake the two new corners.
Analyze· about 32 minutes by hand· 5 steps
Given
Parcel: TRACT 7, four corners, US survey feet, northing first.
A N 4700.00 E 6200.00
B N 5100.00 E 6500.00
C N 4820.00 E 7040.00
D N 4280.00 E 6760.00
Boundary courses: A-B N 36°52′12″ E 500.00 ft; B-C S 62°35′33″ E 608.28 ft; C-D S 27°24′27″ W 608.28 ft; D-A N 53°07′48″ W 700.00 ft.
The owner wishes to sever exactly 3.000 acres from the A-B end of the tract.
The cut line must run parallel to the A-B frontage. Call its intersection with side A-D point A′ and its intersection with side B-C point B′.
Required
The perpendicular offset h of the cut line from A-B.
Coordinates of A′ and B′, and the length and bearing of the new line A′ - B′.
The area of the remainder.
Work it through yourself before reading on - the solution below shows every step, so there is no way to skim it without giving the answer away.
Premium
The worked solution is part of Premium
This problem is 5 steps of computation, with the arithmetic shown at every stage and an independent check at the end. Several problems from every category are free to read in full so you can judge the format first.
Every calculator, the whole reference library and all the guides are free to use forever - the practice bank, the full problem library and the printable job paperwork are the paid upgrade.