Prove that there are infinitely many points on a line Prove

Prove that there are infinitely many points on a line. Prove that there are infinitely many lines through a point.

Solution

Let\'s assume that end points are A(0,0) and B(1,0).

Find a point in between them.

C=(0.5,0)

Now try finding another point. D(0.8,0)

We can always find another point.

Because there are infinite numbers between 0 and 1 (just think of decimals).

In the same way there are infinite points in a line segment.

(b)

We can draw exactly one line through two points.

Let us draw a circle around given point \"p\". There must be a line through \"p\" and each point on the circumference of the given circle.

There are infinitely many points on the circle, so we can draw infinitely many lines through \"p\".