P (a, b) is the midpoint of a line segment between axes. Show that equation of the line is `x/a+y/b=2.`

Explanation

To show that the equation of the line is \( \frac{x}{a} + \frac{y}{b} = 2 \) given that \( P(a, b) \) is the midpoint of a line segment between the axes, we can follow these steps:

### Step 1: Understand the Midpoint
Let’s denote the x-intercept of the line as \( h \) and the y-intercept as \( k \). The coordinates of the x-intercept are \( (h, 0) \) and the coordinates of the y-intercept are \( (0, k) \). The midpoint \( P(a, b) \) of the line segment connecting these intercepts is given by the formula:
\[ P\left(a, b\right) = \left(\frac{h + 0}{2}, \frac{0 + k}{2}\right) = \left(\frac{h}{2}, \frac{k}{2}\right) \]

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