How do i find the coordinates of D, given that CD is always perpendicular to AB?

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nullbear

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Image for reference: https://pasteboard.co/JnFMUbe.png

If i have 3 points, with coordinates,
How do i find a fourth point, D, which is a point where a line perpendicular to AB and crossing through point C would intersect with line AB?

I know that this could be solved with trig, but i'm fairly confident it could be solved with a single algebraic expression/solution as well.1598195202014.png
 
nullbear said:
Image for reference: https://pasteboard.co/JnFMUbe.png

If i have 3 points, with coordinates,
How do i find a fourth point, D, which is a point where a line perpendicular to AB and crossing through point C would intersect with line AB?

I know that this could be solved with trig, but i'm fairly confident it could be solved with a single algebraic expression/solution as well.
Click to expand...
Please show us the basis of your confidence.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.

1598195108258.png
 
Because it's effectively just a line intercept question. It's a triangle, sure, but it could be solved with "y = mx + b"

where M of CD is actually just "-1/(m of AB)"

I'm no longer stuck on it. And i was wrong in that it can be solved with a single expression, since there are two things to solve for: x, and y.

Essentially:

m(CD)x + b(CD) = m(AB)x + b(AB) then use this to find x, and punch that x into either line to find y.

Where m(CD)x is just (-1/m(AB)) and m(AB) is (x(B) - x(A)) / (y(B) -y(A))
 
So in the case of this image, since the slope of AB is 1:

-x + b(CD) = x + b(CD)
 
nullbear said:
Image for reference: https://pasteboard.co/JnFMUbe.png

If i have 3 points, with coordinates,
How do i find a fourth point, D, which is a point where a line perpendicular to AB and crossing through point C would intersect with line AB?

I know that this could be solved with trig, but i'm fairly confident it could be solved with a single algebraic expression/solution as well.
Click to expand...
The point \(D\) is the intersection of a line through \(C\) & \(\overline{AB}\) with slope the negative reciprocal of the slope of \(\overline{AB}\).
 
Find the equation of line AB. Then find the equation of the line through C that is perpendicular to line AB. Then ....
 
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