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Coordinate Operations

Coordinate Operations. Reminder: Coordinates start at an arbitrary beginning x B = x A + Dep AB y B = y A + Lat AB If the coordinates of A and B are known: Lat AB = y B – y A Dep AB = x B – x A L AB = (Lat AB 2 + Dep AB 2 ) ½ Az x = tan -1 (Dep AB / Lat AB ).

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Coordinate Operations

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  1. Coordinate Operations • Reminder: • Coordinates start at an arbitrary beginning • xB = xA + DepAB • yB = yA + LatAB • If the coordinates of A and B are known: • LatAB = yB – yA • DepAB = xB – xA • LAB = (LatAB2 + DepAB2)½ • Azx = tan-1(DepAB/LatAB)

  2. Coordinate Example • Assign Coordinates • A(600.00, 1800.00) • DepAB = -200.09 • LatAB = -1299.98 • B(399.91, 500.02) • DepBC = 1500.03 • LatBC = -199.70 • C(1899.95, 300.32) • DepCD = -99.94 • LatCD = 1400.01 • D(1800.01, 1700.33)

  3. Coordinates and Lines • Any two points connect a line • Line equation: Y = mX + b • m = slope = (Lat/Dep) = 1/[Tan(Az)] • b = Y intercept = Y – m(X) • Intersection • Each line has its own equation • Intersection point satisfies both • Parallel line have the same m, different b • Perpendicular lines have inverse slopes, sign changes • Say BC is perp. To AB, mAB = 3.50 • mBC = -1/mAB = -0.285

  4. (1800.01, 1700.33) B(399.91, 500.02) (1899.95, 300.32) Lines from Coordinates • Line AB • m = 1/tan(AzAB) = 1/tan(188°45’) = 6.497 • m = Lat/Dep= (500.02 – 1800.00) (399.91 – 600.00) = 6.497 • b = Y – mX= 1800.00-(6.497)(600.00) = -2098.20 • Y = 6.947X – 2098.20

  5. (1800.01, 1700.33) B(399.91, 500.02) (1899.95, 300.32) Coordinates from Lines • Find E, 900.00’ along AB • DepAE = -136.91 • LatAB = -899.53 • E(463.09, 900.47) • Define EF parallel to BC • mEF = mBC = -0.13313 • b = Y – mX = 900.47 - (-.13313)(463.09) = 962.12 • Y = -.13313X + 962.12

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