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Shortest Distance between a Point and a Line (in Angle Bisector)

What do we mean by the distance between a point and a line segment? In the diagram below, what is the distance between point R and line segment AB? Move the sliders to try to make sense of the concept of distance between a point and a line. If we let P be a point on the line segment AB, we see that PR is the "distance between R and AB. But there are many locations for P and different distances for P!

Move point P along AB. Is there a particular position of P on AB where the distance PR is the shortest? What is the angle between PR and AB when the distance is the shortest?

What do we mean when we want to find the distance between R and AB? How do we obtain this distance?

Explore point Q on line segment BC. Adjust the position of Q until you get the shortest distance RQ. (Distance between R and BC) Is RQ = PR? Try moving point R and again find the (shortest) distance between R and AB and R and BC What can we conclude about the line BX ?