Question

Suppose the coordinate of a is 0, ar = 5, and at =7. What are the possible coordinates of the midpoint of rt ?

Answer 1

Here 'a' corresponds to 0.

Now there are two possibilities for 'r' & 't'

Case 1.

They are on the same side to the right of 'a'

In that case 'r'  corresponds to 5 & 't' corresponds to 7.

The midpoint of 'r' and 't' shall be $\frac{5+7}{2} =6$

Case 2.

Both are on the left of 'a'.

In that case 'r' corresponds to -5 & 't' corresponds to -7

The midpoint shall be $\frac{-7-5}{2} =-6$

Case 3.

'r' in on the right of 'a' and 't' is on the left of 'a'

So 'r' corresponds to 5 and 't' corresponds to -7

The midpoint shall be $\frac{-7+5}{2}=-1$

Case 4.

'r' is on the left of 'a' & 't' is on the right of 'a'.

'r' corresponds to -5 & 't' corresponds to 7

The midpoint shall be $\frac{-5+7}{2}=1$

The possible coordinates of the midpoints of rt are 6, -6, 1, -1.