a) Use Coordinate Geometry Computations to compute the intersection point of the lines AB and CD. The X and Y coordinates of stations A, B,C and D in feet are given as follows: XA=8377.66 YA=4340.92 XB=8719.43 YB=4642.65 XC=84.36.76 YC=4712.64 X−{D}=8810.45 YD=4325.72 b. Use an alternative method (e.g. analytical geometry) to compute the intersection point.

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a) Use Coordinate Geometry Computations to compute the intersection point of the lines AB and CD. The X and Y coordinates of stations A, B,C and D in feet are given as follows:  XA=8377.66 YA=4340.92  XB=8719.43 YB=4642.65  XC=84.36.76 YC=4712.64  X−{D}=8810.45 YD=4325.72  b. Use an alternative method (e.g. analytical geometry) to compute the intersection point.

Jordan Mitchell · Accepted Answer

Step 1  a) The Coordinates are as follows:  (XA, YA)=(8377.66, 4340.92)  (XB, YB)=(8719.43, 4642.65)  (XC, YC)=(8436.76, 4712.64)  (XD, YD)=(8810.45, 4325.72)  So,  The equation of line AB becomes  y−4340.92=4642.65−4340.928719.43−8377.66(x−8377.66)  ⇒y−4340.92=0.877(x−8377.66)  1) ⇒y=4340.92+0.877(x−8377.66)  The equation of the line CD becomes  y−4712.64=4712.64−4325.728810.45−8436.76(x−8436.76)  ⇒y−4712.64=−1.041(x−8436.76)  2) ⇒y=4712.64−1.041(x−8436.76)  Now,  For the intersection point of AB and CD, equate equation (1) and (2), we get  4340.92+0.877(x−8377.66)=4712.64−1.041(x−8436.76)  ⇒0.877(x−8377.66)+1.041(x−8436.76)=4712.64−4340.92  ⇒1.918x−16129.88=371.72  ⇒1.918x=16501.6  ⇒x=8603.54  Put the value of x in the equation (1), we get  y=4340.92+0.877(8603.54−8377.66)  ⇒y=4539.02  ∴ we get  Step 2  b) We have  (XA, YA)=(8377.66, 4340.92)  (XB, YB)=(8719.43, 4642.65)  (XC, YC)=(8436.76, 4712.64)  (XD, YD)=(8810.45, 4325.72)  Now,  The direction vector for AB is given by  zAB=⟨8719.43−8377.66, 4642.65−4340.92⟩

Jordan Mitchell · Accepted Answer

Step 1  ⇒(x−x1)=m(y−y1)  =x−x1y−y1=46.40.65−4340.928717.43−8376.66  ⇒x−8717.43y−4640.65=0.877  ⇒(x−8717.43)=0.877(y−4640.65)  1) ⇒0.877y−x+4647.5=0  and  x−x2y−y2=m  (x−8436.76)=4710.64−4321.728436.76−8810.45(y−4710.64)  =(x−8436.76)=−1.04(y−4710.64)  2) ⇒−1.04y−x+13147.42=0  from (1) and (2)  x=−4433.96S  y=−8536.09

a) Use Coordinate Geometry Computations to compute the intersection point

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