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Independent coordinate of point A and B are (60,70) and (70,60) respectively . calculate latitude and departure.
A) L=−10,D=−10
B) L=−10,D=+10
C) L=10(S),D=10(E)
D) Both B and C
Both B and C
Latitude (L) and Departure (D) represent the coordinate differences of a survey line along the North-South and East-West axes, respectively. For a line joining points A to B, Latitude is calculated as YB−YA and Departure as XB−XA. Since L=−10 (South) and D=+10 (East), both Option B and Option C correctly describe these components.
Latitude (L) and Departure (D) represent the coordinate differences of a survey line along the North-South and East-West axes, respectively. For a line joining points A to B, Latitude is calculated as YB−YA and Departure as XB−XA. Since L=−10 (South) and D=+10 (East), both Option B and Option C correctly describe these components.
Latitude (L)=YB−YA=l⋅cos(θ) — Orthographic projection on the North-South meridian
Departure (D)=XB−XA=l⋅sin(θ) — Orthographic projection on the East-West parallel
In surveying, the independent coordinates of a point represent its absolute distance along the X-axis (East/West) and Y-axis (North/South) from an origin. Latitude is the orthographic projection of a survey line on the reference meridian (Y-axis), where positive values indicate North (N) and negative values indicate South (S). Departure is the orthographic projection on the reference parallel (X-axis), where positive values indicate East (E) and negative values indicate West (W).
Positive Latitude is North (+N), and Negative Latitude is South (-S).
Positive Departure is East (+E), and Negative Departure is West (-W).
Consecutive coordinates (differences) are calculated by subtracting the preceding point's independent coordinates from the succeeding point's independent coordinates.
Provides a systematic sign convention for defining directions and vectors in traversing.
Allows simple conversion between cartesian rectangular coordinates and polar coordinates (length and bearing).
Sign errors frequently occur if the order of subtraction (PointB−PointA) is swapped.
Requires proper quadrant mapping to convert back to Whole Circle Bearings (WCB).
Computation of closing errors in closed traverse surveying.
Plotting traverse points accurately using independent coordinates.
Option A gives L = -10, D = -10, which incorrectly assumes Departure is negative (West).
Option B (L = -10, D = +10) and Option C (L = 10(S), D = 10(E)) express the exact same physical quantities using different notation conventions.
Therefore, Option D (Both B and C) is the correct complete choice.
D is correct — Both Option B and Option C represent the exact same coordinate differences using standard numerical (-/+) and directional (S/E) sign conventions respectively.
Always double check whether the question asks for line AB (B−A) or line BA (A−B); reversing the direction flips the signs for both latitude and departure.