 Search # Surveying I– coordinate account

##### Page takes part in the competition "Notes on the Internet" organized by the Rector of Academy of Science and Technology in Cracow. V o t e ! // <![CDATA[ flash("migot", "#FF6600", 500, "#008000", 500); // ]]> ### Calculation of coordinates of a point by a linear intersection  Figure 1. Linear intersection in a coordinate system

Search:
P (XP, YP)

Data:
A (XA, YA)
B (XB, YB)

Measured:
dAP, dBP

To calculate the coordinates of point P on the basis of the coordinates of two points A and B, and measured the length of the sides of the AP and BP use a linear intersection method. First, we sketch by placing a point in a coordinate system (Figure 1.).
We calculate the northing and the easting difference ΔxAB = XB – XA, ΔyAB = YB – YA, which are necessary for determining bearing* AAB oraz długości* boku AB:
DAB = √____________ ΔxAB2 + ΔyAB2

*If you do not remember
- method of calculating the length of the coordinates, click - how to calculate the bearing from coordinates of two points, click To calculate the angles α, β and γ in a triangle ABP use the cosine theorem:

#### DAB2 = dAP2 + dBP2 –2dAPdBPcosγ ⇒ γ = arctg DAB2 –(dAP2 + dBP2)–2dAPdBP dAP2 = DAB2 + dBP2 –2DABdBPcosβ ⇒ β = arctg dAP2 – (DAB2 + dBP2)–2DABdBP dBP2 = dAP2 + DAB2 – 2dAPDABcosα ⇒ α = arctg dBP2 – (dAP2 + DAB2)–2dAPDAB

Ensure you have calculated the sum of the angles is equal to 200g,0000.

In the remainder of the calculations proceed as though the angular intersection.

Calculate the bearing angle of the side AP:

#### AAP = AAB –α

and northing and the easting difference based on the the length and bearing of the side AP:

#### ΔxAP = dAPcosAAP ΔyAP = dAPsinAAP

The final coordinates of point P:

#### XP = XA + ΔxAP YP = YA + ΔyAP

Control calculations are re-enumeration of coordinates of a point P on the basis of point B and compare them with the coordinates of point P calculated on the basis of point A.

Calculate the bearing angle of the side BP:
ABP = AAB + β

and northing and the easting difference based on the the length and bearing of the side BP:
ΔxBP = dBPcosABP
ΔyBP = dBPsinABP

The final coordinates of point P:
XP = XB + ΔxAB
YP = YB + ΔyAB

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