Find a point on a line given, distance from startpoint

In summary, to calculate the coordinates for point P on a line L with a distance Z from the startpoint A, use the equation f(x)=y=(y2-y1)/(x2-x1)(x-x1) + y1. If you want the point to be in the direction of endpoint B, replace +/-Z with just Z. Let t = arctan[(y2-y1)/(x2-x1)] to determine the angle of the slope, then replace x in f(x) with x1+(+/-Z)cos(t) to find the coordinates for point P.
  • #1
boston
1
0
Hi,

I have a line L stretching from point A to ponit B. The startpoint A has the coordinates x1, y1 and endpoint B has the coordinates x2, y2.

I want a formula for calculating the coordinates for point P. Point P lies on the line L and with the distance Z from startpoint A.

BR Boston
 
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  • #2
your equation is f(x)=y=(y2-y1)/(x2-x1)(x-x1) + y1 [this is just using y-y0 = m(x-x0)]

Now, a distance Z should be determined by a displacement +/-Z. There are two answers as written, if it is meant "in the direction of b" then replace +/-Z with just Z

Let t = arctan[(y2-y1)/(x2-x1)], this is the angle of the slope.

Then replace x in f(x) with x1+(+/-Z)cos(t). That is, you are finding y when x is at the point when you are +/-Zcos(t) from the coordinate x1. That is how much it changes when you move up or down the slope a displacement of +/-Z. Your point is (x1+(+/-Z)cos(t), f(x1+(+/-Z)cos(t))
 
Last edited:

1. How do I find a point on a line given a specific distance from the starting point?

To find a point on a line given a distance from the starting point, you can use the distance formula: d = √((x2-x1)^2 + (y2-y1)^2). Plug in the coordinates of the starting point (x1, y1), and the distance from the starting point (d), and solve for x2 and y2 to find the coordinates of the desired point.

2. Do I need to know the slope of the line to find a point at a specific distance from the starting point?

No, you do not need to know the slope of the line to find a point at a specific distance from the starting point. The distance formula works for any type of line, whether it is horizontal, vertical, or diagonal.

3. Can I use the Pythagorean Theorem to find the coordinates of a point on a line given a distance from the starting point?

Yes, you can use the Pythagorean Theorem to find the coordinates of a point on a line given a distance from the starting point. The distance formula is essentially a variation of the Pythagorean Theorem for finding the distance between two points on a coordinate plane.

4. What if the starting point is not at the origin (0,0)? Can I still find a point at a specific distance from it?

Yes, you can still find a point at a specific distance from the starting point even if it is not at the origin. You will just need to use the coordinates of the starting point in the distance formula instead of assuming that it is (0,0).

5. Is there a specific method or formula for finding a point on a line at a specific distance from the starting point?

Yes, there is a specific formula for finding a point on a line at a specific distance from the starting point. It is called the distance formula and is d = √((x2-x1)^2 + (y2-y1)^2), where (x1,y1) is the starting point and (x2,y2) is the desired point at the given distance (d).

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