Hello,

Let and

The equation of the variable line is :

But we know that it's passing through (5,0).

Thus

-->

Therefore, the equation of the variable line is : , a is the variable

So we know that :

Because H and K are on this line.

Plus, H is on the line of equation

And K is on the line of equation

--->

By substituting (1) into (3), you will have with respect to a.

Replace this expression of in (1) to have with respect to a.

Do the same for and .

Then, the midpoint of HK is , which will be coordinates with respect to a

Hope that helps... If you have questions about some steps, don't hesitate ^^