Known: point A, length line, angle (radian)... point b?

Hi,

Question 1:

If a draw a line from (1,1) to (2,1) what angle does that line have in radians(relative to pi)? I think 0*pi

Same for lets say (1,1) to (1,2) I think pi/2

or even (1,1) to (2,2) (Please use this correct answer in question 2 because I might have it wrong) I think pi/4

Question 2:

I need to draw a line with given info: coords point A, an angle (radian relative to pi) and length of line.

I think the solution lies using algebra on the Pythagorean theorem.

Example: What are coords of point B?

coords point A = (1,1)

angle = pi/4 (45 degrees) {Note that this may not be what I mean which is why I asked the first question)

length = sqrt(2) ~ 1,41

The answer should be (2,2) but the point is that I need to understand the algebra behind it so I can use it for more complex variables/parameters.

Re: Known: point A, length line, angle (radian)... point b?

Quote:

Originally Posted by

**Vibonacci** Question 2:

I need to draw a line with given info: coords point A, an angle (radian relative to pi) and length of line.

I think the solution lies using algebra on the Pythagorean theorem.

Example: What are coords of point B?

coords point A = (1,1)

angle = pi/4 (45 degrees) {Note that this may not be what I mean which is why I asked the first question)

length = sqrt(2) ~ 1,41

The answer should be (2,2) but the point is that I need to understand the algebra behind it so I can use it for more complex variables/parameters.

Given the points $\displaystyle (1,1)~\&~(2,2)$ the distance between them is $\displaystyle \sqrt{(2-1)^2+(2-1)^2}=\sqrt{2}$

The slope between is $\displaystyle 1$ so $\displaystyle tan(\theta)=1$ or $\displaystyle \theta=\frac{\pi}{4}$.

That is the algebra behind it.

Re: Known: point A, length line, angle (radian)... point b?

Thanks for the answer!

so in my example the slope is tan(p/4) = 1. Thanks.

However I think I should rephrase my question as I still don't know how to use the distance formula in combination with the slope to get my answer (coords of point b).

You started with the distance formula but it can only be used if you know the coords of point b and that is what is unknown. Distance is known in advance though.

So lets say we have point a(1,1), slope = tan(pi/5), and distance/length of line = 2.

How do I calculate the coords of point b (end of line segment)?

Re: Known: point A, length line, angle (radian)... point b?

Quote:

So lets say we have point a(1,1), slope = tan(pi/5), and distance/length of line = 2.

How do I calculate the coords of point b (end of line segment)?

point b will have coordinates ...

$\displaystyle (x,y) = \left(1 + 2\cos{\frac{\pi}{5}} , 1 + 2\sin{\frac{\pi}{5}}\right)$

Re: Known: point A, length line, angle (radian)... point b?