Find the coordinates of the points (A,B) where the line 5x + y = 10 cuts the x -axis and y -axis respectively. Further, find the coordinates of the midpoint of AB.

Given: The line 5x + y = 10 intersects the x-axis at point A.

Thus y-coordinate of A = 0.

And the line 5x + y = 10 intersects the y-axis at point B

Thus the x-coordinate of B = 0.
Now, let us substitute y = 0 in 5x + y = 10 to get the x-coordinate of point A, 
$\begin{array}{l}5\mathrm{x}+0=10\\ \Rightarrow \mathrm{x}=\frac{10}{5}\\ \Rightarrow \mathrm{x}=2\end{array}$ 
Hence, the coordinates of point A= (2, 0).

Also, let us substitute x=0 in 5x+y=10 to get the y-coordinate of point B.
 
$\begin{array}{l}5\times 0+\mathrm{y}=10\\ \Rightarrow \mathrm{y}=10\end{array}$ 
Hence, the coordinate of point B=(0, 10).

Now, we know that, 
Midpoint of any two points, say $\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)$ and $\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)$  is $\left(\frac{{\mathrm{x}}_1+{\mathrm{x}}_2}{2},\frac{{\mathrm{y}}_1+{\mathrm{y}}_2}{2}\right).$ 
Hence, the midpoint of AB using the midpoint formula is:

$\left(\frac{2+0}{2},\frac{0+10}{2}\right)$
$=\left(\frac{2}{2},\frac{10}{2}\right)$

$=\left(1,5\right)$ 
Therefore, the coordinates of points A and B are (2, 0) and (0, 10) respectively, and the coordinates of the midpoint AB is (1, 5).