Question

a line is a set of all points that:

a. have the same sum of distances from two points.

b. are the same distance from one point.

c. have the same difference of distances from two points

d. are the same distance from two points

Explanation:

Step1: Analyze Option A

Sum of distances from two points - this is the definition of an ellipse, not a line.

Step2: Analyze Option B

Same distance from one point - this is the definition of a circle, not a line.

Step3: Analyze Option C

Same difference of distances from two points - this is the definition of a hyperbola, not a line.

Step4: Analyze Option D

A line is the set of all points that are equidistant (same distance) from two given points. For example, the perpendicular bisector of a line segment is a line where every point on it is equidistant from the two endpoints of the segment.

Answer:

D. are the same distance from two points