CODEWITHSUNDEEP
iosobjective-cmathtrigonometry
Benjamin
Benjamin

Reputation: 663

How to find a point along an vector at an variable distance

I need to find the value along a vector for a given x coordinate. Like so;

enter image description here

I know the values of A, B and C. All of these value are variable. I need to calculate X. I know this is possable I just can't remember my trigonometry lessons. I'm aware of similar questions like this one but it only finds the mid-point.

Thank you.

Upvotes: 0

Views: 3181

Answers (3)

tom10
tom10

Reputation: 69192

For a line through the origin, as you have in the picture, you can use the idea of similar triangles:

X_y = B_y * (X_x/B_x)

Or, for the numbers shown in the example, X_y = 50, and X=(50,50).

To understand this, similar triangles says:

X_y/X_x = B_y/B_x

since triangles with similar shapes (ie, that have the same angles), have the same ratios; and the first formula is just solving the second to give X_y.

(If the line isn't through the origin, first subtract A from everything, then calculate X_y as above, then add A to everything.)

Upvotes: 1

Captain Skyhawk
Captain Skyhawk

Reputation: 3500

  y = ||C-A|| / ||D-A||
  Z = (B - A) * y

Where y = length of vector C minus vector A, divided by length of D(unlabeled original length along x axis) minus vector A

Upvotes: 1

Abhineet Prasad
Abhineet Prasad

Reputation: 1271

Lets say A(x1,y1) and B(x2,y2)

and co-ordinates of X(x,y) , then:

y = ((y2-y1)/(x2-x1))x + c .....(1)

where c is the y intercept, which in this case is 0.

Upvotes: 2

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