Rihan marked a point on a piece of paper. How many lines can he draw that pass through the point? Sheetal marked two points on a piece of paper. How many different lines can she draw that pass through both of the points? Can you help Rihan and Sheetal find their answers?
Rihan's Answer: Rihan can draw infinitely many lines passing through a single point.
Sheetal's Answer: Sheetal can draw exactly one line passing through two distinct points. Reason: Any two points determine a unique line that passes through both of them.
Explanation
The chapter explains that a point determines a precise location. When only one point is given, there is no constraint on the direction of the line, so infinitely many lines can pass through it. However, when two points are marked, the chapter states: 'Observe that any two points determine a unique line that passes through both of them.' This fundamental property of geometry means exactly one line can be drawn through any two given points.
Solution Steps
Through a single point, infinitely many lines can be drawn.
Through two distinct points, exactly one line can be drawn.
Any two points determine a unique line that passes through both of them.