Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: coordinates
Posted:
Nov 26, 2002 1:17 AM


James wrote:
> POINT A HAS COORDINATES OF 10000.00 AND 10000.00 > point b has coordinates of 10070.707 AND 10070.707 > what is the bearing and distance from point a to point b ?
Doing homework are you? First important thing that we're assume, is that we're working in R2 Cartesian coordinates, so every point requires only two values x,y, to specify its location. Everything is located on the Cartesian plane.
Let's try a similar problem.
Let point C be at (1,2). Let point D be at (11,3)
Then the distance from point C to D is sqrt[(1 11)^2 + (2  3)^2] = sqrt(12^2+5^2) = sqrt(144+25) = sqrt(169) = 13.
So D is 13 units from C.
What is the bearing? Using 0 degrees = horizontal line to right, 90 degrees = line straight up, 180 degrees = horizontal line to left and 270 degrees line straight down, we have to use some type of trigonometry to figure out the bearing.
So some function, say sin(angle) or cos(angle) or tangent(angle) is necessary.
Working with the x,y values, we probably can use the tangent function, say y/x. For the bearing from C to D we change 12 units along the xaxis, and we drop 5 units down along the yaxis, so we have, by drawing a picture out, some angle between 180 and 270 degrees, located in the 3rd quadrant.
It is always important to roughly sketch the picture out, so we know exactly which of the 4 quadrants the angle is in.
Then we can (almost) blindly apply trigonometry, and in this case we have tangent(angle) = 5/12 so angle = arctangent(5/12) = 0.394791... radian or using the fact that 180 degrees = Pi radians, we have 22.619864... degrees. We add 180 degrees to this angle to get 202.6198649... degrees which is the bearing of point D from point C.
Now I've given you a worked out example, you can solve your question, with hardly any labor on your part. So please do it.
Thanks!



