Question

If P(r, c) is midpoint of a line segment between the axes then show that `x/"r" + y/"c"` = 2

Answer 1

Let AB be the line segment intercepted between the axes.

Let A be (a, 0) and B be (0, b)

Given P(r, c) is the midpoint of AB

∴ (r, c) = `((0 + "a")/2, ("b" +0)/2)`

r = `"a"/2`, c = `"b"/2`

a = 2r, b = 2c

The equation of the line AB having x-intercept a and y-intercept b is  `x/"a" + y/"b"` = 1

Substituting for a, b in the above equation, we have

`x/(2"r") + y/(2"c")` = 1

`x/"r" + y/"c"` = 2