User:EML4500.f08.delta 6.ramirez/pointcoordinates

The following are the unknown variables that will be determined:

(XD, YD) (XB, YB) (XC, YC)

We will begin by finding the coordinates of point D. Note: Point A has been designated as the origin.

Using the definition of line AD, (XD, YD) can be found.

$$\vec{AD} = (X_{D} - X_{A}) \vec{i} + (Y_{D} - Y_{A}) \vec{j}$$

Since point A is referenced as the origin, XA and YA are equal to zero.

By definition of the displacement vector of A,

$$\vec{AD} = d_{3}\vec{i} + d_{4}\vec{j}$$

Thus,

(XD, YD) = (d3, d4) = (4.352, 6.1271)

Next, using the relationship of two points on the same line gives,

$$y - y _{C} = tan(\theta) (x - x_{C})$$

where θ = 30°, (XC, YC) = (5.92, 3.42)

The relationship between point B and point D gives,

$$y - y _{B} = tan(\theta + \frac{\pi }{2}) (x - x_{B})$$

where θ = 135°,(XB, YB) = (-0.88, 0.88)

Results:

Point D: (4.35, 6.13) Point C: (5.92, 3.42) Point B: (-0.88, 0.88)