Question

The following EN and XY coordinates for points A through C are given. In a 2D conformal coordinate transformation, to convert the XY coordinates into the EN system, what are the: (a) Scale factor? (b) Rotation angle? (c) Translations in X and Y? (d) Coordinates of points C in the EN coordinate system? State Plane Coordinates (m) Arbitrary Coordinates (ft) Point 111,493.468 111,844.860 719,542.829 4873.67 6609.04 720745 719,899.341 6402.92 7041.22 603723

Answer 1

a) Scale factor:

$s=\sqrt{\frac{(E_B-E_A)^2+(N_B-N_A)^2}{(X_B-X_A)^2+(Y_B-Y_A)^2}}$

(719899.341-719542.829)2(111844.86 111493.468)2 (6402.92 -4873.67)(7207.45 6609.04)2

0.30483

b) Rotation angle:

$\theta =\alpha +\beta$

α = tan-1 (XA-XB 4873.67-6402.92 -1 = tan 6609.04- 7207.45 248.630

= tan-1 (EL-EB + C 1719542.829- 719899.341 = tan--Ty| 111493.468 111844.860 844.860 +18o 225.410

CALCULATE THE VALUE OF $\theta$ BY SUBRACTING $\beta$ FROM $\alpha$

θ-225.41-248.63 -23.22. _

Add 360 to make positive

Rotational angle = $336.78^{\circ}$

c) Translation in X and Y

Tanslation in X

$T_X=E_A-(S*X_ACos\theta -S*Y_ASin\theta )\\ =719542.829-(0.304*4873.67Cos(336.78)-0.304*6609.04Sin(336.78))\\ =719542.829-2153.71\\ =717389.119$

$T_Y=N_A-(S*X_ASin\theta -S*Y_ACos\theta )\\ =11149.468-(0.304*4873.67Sin(336.78)-0.304*6609.04Cos(336.78))\\ =13580$

d)

Coordinates of EC

(0.304 * 7041 .22COs(336.78)一0.304 * 6037.23Sin (336.78)) 71 7389.1196 720079.86

Coordinates of NC

13580 (0.304 * 7041 .22Sin (336.78)-0.304 * 6037.23COs(336.78)) 11049.41