Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

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Solution

A line is defined as a straight path that extends infinitely in two directions.

In the given image $4$ points are shown $A, B, C$ and $D$ .

$∴$ The possible ways for naming the line are

$\leftarrow \to A B, \leftarrow \to A C, \leftarrow \to A D,$ $\leftarrow \to B C, \leftarrow \to B D,$ $\leftarrow \to C D$

But we know that we can write a line $\leftarrow \to A B$ as $\leftarrow \to B A$ also.

Hence, the possible twelve ways for naming the lines are

$\leftarrow \to A B, \leftarrow \to A C, \leftarrow \to A D,$

$\leftarrow \to B C, \leftarrow \to B D, \leftarrow \to B A,$

$\leftarrow \to C D, \leftarrow \to C A, \leftarrow \to C B,$

$\leftarrow \to D A, \leftarrow \to D B, \leftarrow \to D C$

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Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

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