32. P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is <math><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>a</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>y</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mn>2</mn></mrow></math> .

32. Since P (a, b) is the mid-point of the line segment say AB with points A (0, y) and B (x, 0) we can write, (a, b)= (x+02, y+02)⇒a=x2 b=y2⇒x=2a y=2bSo, the equation of line with x and y intercept 2a and 2b using intercept form isx2a+y2b=1⇒xa+yb=2Hence, proved

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32. P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is $\frac{x}{a} + \frac{y}{b} = 2$ .

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alok kumar singh | Contributor-Level 10

4 months ago

32.

Since P (a, b) is the mid-point of the line segment say AB with points A (0, y) and B (x, 0) we can write,

$(a, b) = (\frac{x + 0}{2}, \frac{y + 0}{2})$

$\Rightarrow a = \frac{x}{2}$

$b = \frac{y}{2}$

$\Rightarrow x = 2 a$
$y = 2 b$

So, the equation of line with x and y intercept 2a and 2b using intercept form is

$\frac{x}{2a} + \frac{y}{2b} = 1$

$\Rightarrow \frac{x}{a} + \frac{y}{b} = 2$

Hence, proved

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32. P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is $\frac{x}{a} + \frac{y}{b} = 2$ .

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32. P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is $\frac{x}{a} + \frac{y}{b} = 2$ .