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Ryan, Engineer
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Experience:  B.S. in Civil Engineering
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# I have a piece of property that I want to divide into two

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I have a piece of property that I want to divide into two equal portions. The property has 5 corners. I can provide the lat/lon for each corner and the length of all 5 sides. I want to split two opposite sides into two equals portion to start----front and back boundary lines. I then want to know where the point needs to be between those two points to end up with two equal portion of acreage. This a mathematical exercise--not a legal matter. Once I have a math expert I can provide a diagram and the data points.

Thank you for your question.

Please describe the situation a little more. A diagram or plat depicting the property and surrounding roads would be helpful.

Customer: replied 7 months ago.
This is a mathematical endeavor, not a legal issue. the property has 5 sides. it needs to be divided in half--equal portions. The front side has the assess road to the property. The back side provides the exit access to national forest property. Each portion must be equal acreage. I want to divide the front and rear property boundary to be divided equally. If you do that and draw a boundary line between the from and rear boundary lines the property will be split in two parcels but not equal acreage. Some somewhere between the line from front to rear the line possibly at or near the center of that line needs to be moved left or right to insure equal acreage. A calculus expert could do this easily.

This is more of a geometry than a calculus question. Please post a diagram and I will ask the site to move this to math experts if I don't see a simple answer.

Customer: replied 7 months ago.
Geometry to a degree but it is absolutely a calculus solution.

Thank you.

Some of the lines look wavy or curved in the diagram. Are they all supposed to be straight lines? Does any lie run due N-S or E-W?

Is the E line 540 or 542?

You want a front lot and a rear lot, is that correct?

Customer: replied 7 months ago.
The border lines are all straight. I consider the front of the lot to be the 200'side along the access road to the lot. The 80' side is the rear of the lot with access to the national forest. The side you ask about is 542. None of the sides run directly N,S,E or W--not that that should matter.
I want the lot split from front to rear. Each lot would have a 100' front and 40' rear with equal acreage.
Customer: replied 7 months ago.
Better drawing. The dotted line represent about how the property would be split.

Hi,

Thank you for using the site. This is quite an interesting problem.

I have looked at both diagrams that you attached. The first one showed bearings on two of the existing property lines, although only one was readable when I printed it out. Do you have bearings for all five property lines? The angles will make a difference in the area calculations.

Also, do you have any preference about the angle that the new property line meets the 200 foot and 80 foot lines at? For example, at the "front" road, does the new property line need to be perpendicular to the roadway?

It may also turn out that there are multiple solutions, given that the two "new" property lines aren't really constrained, other than having to have one end at the midpoint of an existing property line, and meeting at the other end. If there are any preferences about the shapes of the two new lots, that information might be helpful in narrowing things down to a single solution.

Thanks,

Ryan

Customer: replied 7 months ago.
I do not have the other bearing points at home where I am at now. The original plot diagram is at my cabin where the land is located. I will get them the next time I go up there. You seem to have the gist of the dilemma now. The shape of each new lot
has some significance. There are two cabins on the existing lot. The idea is to split the property and create two new deeds.
Going from the front boundary to the rear serves that purpose but results in the two new lots having very different acreage. It appears the one lot would be closer to 2 acres and the other around 1 acre. The is why the new, center boundary line needs to be moved to the left somewhere in the middle to equalize the size of the lots. Your asking great questions.

Ok, no problem. Whenever you can get the bearings, I can proceed. There are some surveying techniques for calculating areas of weird shapes like this, but the bearing of each line is needed.

Customer: replied 7 months ago.
Okay--I will get you those angles.

Alright, sounds good. :)

Customer: replied 4 months ago.
The property has 5 sides--lot 3. I now have all of the information you should need to determine how to divide this parcel into two equal lots. the front line is 200 feet and the rear property line is 80 feet. The front line should be divided equally into two 100 foot segments and the rear line should be divided into two segments each 40 foot long. Those two center points need to be connected so that I end up with two equal parcels That obviously will result in two new segments that join somewhere in the middle. I need to know the length of those segments and the bearings for each segment.

Hi,

I'm sorry about the delay in replying to you. I had to leave my desk for a time.

Given the irregular shape of the parcel, the lengths and bearings of each of the five sides will be needed to calculate the areas. Without that information, I can't even total area of the existing parcel.

Is there a new diagram?

Thanks,

Ryan

Customer: replied 4 months ago.
see diagram

We're making progress.

Do you have bearings for the 200' and 80' sides? It looks like there is one for the centerline of the (presumed) roadway along the 200 ft side.

Ryan

Customer: replied 4 months ago.
Ryan
No I do not. That is what I have that was recorded by the surveyor numerous years ago before I purchased the property. Are you sure you need those? Going back many years ago to my trig and calculus classes it seems as though those bearing would not be required.
Customer: replied 4 months ago.
RyanI checked with the assessors office where the plat is recorded and there is no bearing recorded for the back boundary line. So, I assume it is not necessary since the other 4 bearings are recorded and the distance of the back boundary is known.

If I could get the bearing for the roadway along the 200 foot side, then I can figure out the bearing for the 80 foot side.

I need the bearings to determine the coordinates of the corner points of the existing boundary.

Customer: replied 4 months ago.
Ryan--I assume you are working on my problem--RIGHT??

Hi,

I'm sorry about the delay in replying to you. I was not aware that you had posted a reply.

I was hoping that you would be able to get the bearing for the street shown at the bottom of the diagram. I can see where there is a bearing recorded, but it is cut off in the portion that you sent. I'll see what I can do with the information available.

Ryan

Customer: replied 4 months ago.
It is 161 80'

161 80´ is the length of the side of the adjacent lot (Lot 7). In the lower left is the last part of a bearing for the dashed centerline of the street. It looks like it ends with an "E".

I'll see if I can figure it out mathematically, but it will take several calculations to do that.

Customer: replied 4 months ago.
Okay--I got ya. I will have to call the assessor's office tomorrow.

Hi again,

After a lot of calculations and some computer programming, I believe that the missing bearing for the roadway to the south of the lot should be very close to N 72º 47' E. From the portion of the bearing that was shown in the diagram, it appears that the last two digits are either 17 or 47, and the above bearing gave me the closest accuracy in closing the entire traverse around the lot. If the value that you get back from the assessor is different from this, then I might need to recalculate the results given below.

Once I had that, I was able to calculate the current area of the lot: 123,604 square feet, or around 2.8 acres.

There are likely a variety of points that would work to divide the lot into two equal portions. I somewhat arbitrarily selected a point along the line running due east from the intersection of the 314.3 foot and 353.77 foot boundaries on the west side of the property, and then determined how far from that corner point you would have to move to set a marker that divides the lot.

Here are three bearings:

1) From the intersection of the 314.3 foot and 353.77 foot sides: Due east, 140.447 feet

2) From the midpoint of the 200 foot boundary: N 18º 33' W, 309.86 feet

3) From the midpoint of the 80 foot boundary: S 15º 31' W, 276.69 feet

Please let me know if you have any additional questions about this.

Thanks,

Ryan

Customer: replied 4 months ago.
Okay--I am in NE right now but when I get back I will get the missing bearing and verify your number. Could you draw in the new segments on the plot diagram and send it to me?
Customer: replied 4 months ago.
Your results appear to be exactly what I was looking for.
Customer: replied 4 months ago.
By the way I am very pleased and impressed with your work.

Yes, I'll send you a diagram as soon as I can.

I have attached the new diagram showing the subdivided lot. (A link will appear following this message.)

The shape of these two lots may not be precisely what you had in mind. As I mentioned, I arbitrarily set the point of intersection to be along the line that extends east from the westernmost point of the property. If you want to adjust the shapes of the lots in some way, I would need some direction or indication as to additional constraints.

Thanks,

Ryan

Customer: replied 4 months ago.
What you did is exactly what I was hoping for. Are the two lots equal in acreage?

Yes. Down to a few square feet, depending on the accuracy of the actual surveying.

Customer: replied 4 months ago.
Okay -- great. I still need to verify thee front bearing---right?

I would advise you to check the bearing I calculated (N 72 deg 47 min E) against what the assessor has on file before you pay anybody to go out and set a marker. If there is a difference then I would need to re-calculate the dividing lines.

Customer: replied 4 months ago.
I agree. I will call tomorrow and let you know.

Ok, sounds good.

Customer: replied 4 months ago.
You are extremely good. I love math and at one time I was too but not as good as you.

Awww, shucks... :)

Customer: replied 4 months ago.
Ryan---I checked with the assessors office and they said the front bearing is N 23 deg. 56 min.When you redo the map could extend the line all the way from the left side of the lot to the right side with both distances?

N 23 deg 56 min W is the bearing of the line between Lot 3 and Lot 7. That one was shown clearly on the original map.

What we need is the bearing of the centerline of the roadway that runs along the south side of the property.

Customer: replied 4 months ago.
I agree.
Customer: replied 4 months ago.
I checked with her again and the bearing you caculated is exactly right. You have absolutely delivered what I requested. Could you give me the length of the line to the right side of the property and the two segments on the right side.

Yaaaay. I was pretty sure I had it right, just because it was the only bearing that fit. But it's nice to have it confirmed.

I'll get those other numbers to you as soon as I can. I'll have to do some calculating to get them, and I'm away from my desk at the moment.

Ryan

Customer: replied 4 months ago.
Thanks.

Hi again,

I have attached an updated diagram of the lot division. Please let me know if there is anything else that I can do to help you with this.

Thanks,

Ryan

Customer: replied 4 months ago.
Absolutely perfect-----great work.Thanks......
Customer: replied 4 months ago.
I guess I have to wait for a mail message to rate you so you get paid----right???

I sent a message to the category moderator regarding the rating issue. There doesn't seem to be anything that I can do on my end to cause the system to deliver a new email message to you. Don't worry about it though, I'm sure it will get straightened out eventually.

Customer: replied 4 months ago.
Ryan----I called them an hour ago and they input the ratings (excellent ) for me and I also added 20 dollars extra for you. Thanks again for great service.

Oh, ok. Thank you for that. I don't see any indication of that on my end (yet), so it may just be a while before the system catches up.

Ryan, Engineer
Category: General
Satisfied Customers: 8992
Experience: B.S. in Civil Engineering
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