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What are perpendicular bisectors?

A line that is perpendicular to the segment of a plane and passes through the midpoint.


What two-dimensional figure results from slicing a right triangular prism with a plane perpendicular to its bases?

what two- dimensional figure results from slicing a right triangular prism with a plane perpendicular to its bases


What figure has a length and width and no depth?

A plane figure.


What has length and width but no thickness?

A plane figure


Given two points A and B in the three dimensional space what is the set of points equidistant from A and B?

A plane is the set of all points in 3-D space equidistant from two points, A and B. If it will help to see it, the set of all points in a plane that are equidistant from points A and B in the plane will be a line. Extend that thinking off the plane and you'll have another plane perpendicular to the original plane, the one with A and B in it. And the question specified that A and B were in 3-D space. Another way to look at is to look at a line segment between A and B. Find the midpoint of that line segment, and then draw a plane perpendicular to the line segment, specifying that that plane also includes the midpoint of the line segment AB. Same thing. The set of all points that make up that plane will be equidistant from A and B. At the risk of running it into the ground, given a line segment AB, if the line segment is bisected by a plane perpendicular to the line segment, it (the plane) will contain the set of all points equidistant from A and B.


Is a taut piece of thread a point line line segment ray or plane?

None of them since a thread has a finite length and finite width. A point has neither length nor width whereas a line, line segment and ray do not have any width. A plane has infinite length and width. The nearest approximation is a line segment.


What figure is formed by the intersection of this cube and the plane and is perpendicular to four of the cubes sides?

square


Which figure is formed by the intersection of a cube and a plane which is perpendicular to four of the cubes sides?

a square


What solid figure has the same cross section when its sliced by a plane parallel to its base as when it is sliced by a plane perpendicular to its base?

Sphere


When is a line perpendicular to a plane?

A line is perpendicular to a plane when it is perpendicular on two lines from the plane


What do you use to find the length of a segment on a coordinate plane?

You use the distance formula.


Does a line have infinite length?

A line does have infinite length because it exists on an infinite plane. The only time it does not have infinite length is when it is a line segment.