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