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If you translate (move without rotation) a copy of the line towards the curve, the first point where the line touches the curve (the tangent to the curve with the slope of the original line) will be the point on the curve closest to the line.
Draw a connecting line from this tangent point to the original line, intersecting that original line at right angles.
Measure the connecting segment. It is the shortest distance.
Vector analysis will give a mathematically strict solution, I do not have the ability to explain this in sufficient detail.
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What figure do you get if you join two points in cartesian plane?
You get a curve. If you join them along the shortest [Euclidean] distance between them, you get a straight line.
A imaginary line that follows the curve of the earth the shortest distance between two points on a globe?
... is called a Great Circle arc.
Why is the shortest distance between 2 points a straight line?
When you curve the line you are travelling you are no longer going directly from one point to the other. If you want to go from one point to another you would want to go directly to the second point.
Is curve the opposite of straight?
Curve is one possible opposite of straight if straight refers to line that does not bend. Other meanings of straight like honest, heterosexual, and direct have different opposites than curve.
What t words is define in geometry as a straight line that touches a curve but continues on with croosing it?
A tangent, but it (a) has nothing to do with croosing (whatever that may mean); and (b) while it does not cross the curve in the neighbourhood of the point of contact - there is no restriction on it crossing the curve at a distance.
