Describe the locus of all points, in space, that are 5 cm from line p.
a. a line, 5 cm from line p.
b. a pair of parallel lines, each parallel to and 5 cm from line p.
c. a sphere with a radius of 5 cm.
d. a cylinder with a radius of 5 cm.
D?
Looks good to me.
Thanks!
The correct answer is d. a cylinder with a radius of 5 cm. The locus of all points that are 5 cm from line p forms a cylindrical shape around line p. This is because a cylinder is a three-dimensional shape with circular bases and a constant distance (radius) between the bases. In this case, the bases of the cylinder would be parallel to line p, and the cylinder would have a radius of 5 cm.
To determine the locus of all points that are 5 cm from line p, we can employ a geometric approach. Let's consider a point A on line p, and let B be any point that is 5 cm away from line p. We can start by drawing a line segment AB and then constructing the perpendicular bisector of AB.
This perpendicular bisector, which we'll call line q, will include all points that are equidistant from both points A and B. Since point A is on line p and all points on line p are equidistant from it, line q will be perpendicular to line p.
Now, let's consider another point C on line q that is 5 cm away from line p. If we draw a line segment BC, we can observe that all points on this segment are equidistant from both line p and line q. Therefore, the locus of all points that are 5 cm from line p is a pair of parallel lines that are each parallel to and 5 cm away from line p.
Hence, the correct answer is b. a pair of parallel lines, each parallel to and 5 cm from line p.