Final answer:
The x-coordinate of the midpoint of the horizontal segment with endpoints (-20,0) and (20,0) is calculated using the midpoint formula and is found to be 0. The perpendicular bisector of a side of a triangle is the line that is perpendicular to that side and passes through its midpoint.
Step-by-step explanation:
To calculate the x-coordinate of the midpoint of a horizontal segment with endpoints (-20,0) and (20,0), we can use the midpoint formula for coordinates, which is ((x1 + x2)/2, (y1 + y2)/2). In this case, x1 is -20 and x2 is 20. Applying the formula for the x-coordinate gives us:
(-20 + 20)/2 = 0/2 = 0.
Therefore, the x-coordinate of the midpoint is 0, which corresponds to option (b).
Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by a compass and straightedge construction. The midpoint of a line segment, embedded in a plane, can be located by first constructing a lens using circular arcs of equal (and large enough) radii centered at the two endpoints, then connecting the cusps of the lens (the two points where the arcs intersect).
The point where the line connecting the cusps intersects the segment is then the midpoint of the segment. It is more challenging to locate the midpoint using only a compass, but it is still possible according to the Mohr-Mascheroni theorem.