The distance d of point P to the line through points A and B is the length compo

Question

The distance d of point P to the line through points A and B is the length component of AP that is orthogonal to AB, as indicated. So the distance from P =(4,4) to the line through the points A=(0,4) and B= (-5,4) is: The distance d of point P to the line through points A and B is the length component of AP that is orthogonal to AB, as indicated. So the distance from P =(4,4) to the line through the points A=(0,4) and B= (-5,4) is: The distance d of point P to the line through points A and B is the length component of AP that is orthogonal to AB, as indicated. So the distance from P =(4,4) to the line through the points A=(0,4) and B= (-5,4) is:

Explanation / Answer

Vector AB = B-A = (-5, 0)
Vector AP = P-A = (-4, 0)

The dot product AP.AB gives the value of the length projection of AP on AB multiplies by the length of AB.

So, d*||AB|| = AP.AB = (-5,0).(-4,0) = -5*(-4) + 0*0 = 20

||AB|| = sqrt(0^2 + (-5)^2) = sqrt(0+ 25) = 5

Therefore d = 20 / ||AB|| = 20 / 5 = 4

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