The shortest distance between a point and a line occurs at:
a) infinitely many points
b) one unique point
c) random points
d) a finite number of points
b) one unique point
The shortest distance between a point and a line occurs at one unique point.
To understand why, we need to consider the concept of perpendicularity. A line can be defined by two points, and any line segment on that line can be considered as part of an infinite number of perpendicular lines.
Now, let's consider a point outside of the given line. To find the shortest distance between this point and the line, we can draw a perpendicular line from the given point to the line. This perpendicular line will intersect the given line in exactly one point, creating a right angle between the two lines.
By the properties of right angles, we can determine that the shortest distance between the point and the line occurs at this point of intersection. Hence, the answer is one unique point (option b).
clearly (b)
why was there any question?