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Asked: 2026-05-12T09:54:58+00:00

I actually have two questions, I found the answer to the second and didn’t

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I actually have two questions, I found the answer to the second and didn’t update the diagram. I’m not actually sure if these are possible, they really stumped me.

Question 1:
Given point A and e, the angle of the line A is on relative to the x-axis where 0<=e<360 degrees, how do you calculate the coordinates of B? BA is perpendicular to A’s line and 1 unit long.

SOLVED: I start by taking the unit vector from a parallel to the x-axis and then I rotate it 90 + e degrees.

Question 2:
I’m using this approach. If anyone has any better suggestions, please let me know.

SOLVED: I find the dot product of the vector from step 1 and the normalized vector AC.

Question 3:
This one should be pretty self-explanatory from the diagram. I need to find the coordinates of C given A, B, the angle of BAC and the distance between A and C.

SOLVED: I rotate BA e degrees and then change the magnitude to d.

If anyone spots problems with my solutions, please comment.

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1 Answer

  1. Editorial Team

    Easy if you understand vectors. Learn about how 2D vectors work and you’ll have it. Is that the course you’re taking?

    1. Take the unit vector from e to A, knowing that a unit vector has length 1. Assume l1 = xi + yj. The perpendicular vector has components that are the reverse of l1 with one sign changed. In this case, l2 = -yi + xj.
    2. Take the vector l2 that you got from the first problem and transform it as follows:

    cx = -cos(t)y – sin(t)x
    cy = +sin(t)y + cos(t)x

    where t is the rotation angle in radians.

    I’ll leave the third one for you. Read about 2D vectors and transformations.

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