Final answer:
To locate a point equidistant from (3,8), (5,2), and (-3,-4), one would find the intersection of the perpendicular bisectors of the line segments connecting each pair of points. The provided phrases relate more to calculus and motion problems than to this geometric problem.
Step-by-step explanation:
The student asked to locate the point or points that are equidistant from the three given points: (3,8), (5,2), and (-3,-4). To find such a point, one would typically write equations for the perpendicular bisectors of the segments connecting each pair of points and then find the intersection of these lines, which would be equidistant from all three points.
The phrases offered involve calculus (finding tangent lines to curves at specific times, determining endpoints, and calculating slope), which are techniques for analyzing motion rather than finding equidistant points in geometry. However, they provide examples of mathematical processes involving slope and tangents that may be understood in the context of analyzing motion or graphed functions rather than the geometry problem initially posed by the student.
Cartesian plane, perpendicular bisectors, equidistant
are important concepts in finding a point equidistant from three given points.