13. If three points (h, 0), (a, b) and (0, k) lie on a line, show that <math><mrow><mfrac><mrow><mi>a</mi></mrow><mrow><mi>h</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mi>k</mi></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math> .

13.Since the three points say P (h, o), Q (a, b) and R (o, k) lie on a line.Slope of PQ = slope of QR⇒b−oa−h=k−bo−a⇒ba−h=k−b−a⇒−ab= (k−b) (a−h)⇒−ab=ka−kh−ab+bh⇒ka+bh=khDividing both sides by kh we get, ⇒kakh+bhkh=khkh⇒ah+bk=1

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13. If three points (h, 0), (a, b) and (0, k) lie on a line, show that $\frac{a}{h} + \frac{b}{k} = 1$ .

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alok kumar singh | Contributor-Level 10

4 months ago

13.

Since the three points say P (h, o), Q (a, b) and R (o, k) lie on a line.

Slope of PQ = slope of QR

$\Rightarrow \frac{b - o}{a - h} = \frac{k - b}{o - a}$

$\Rightarrow \frac{b}{a - h} = \frac{k - b}{- a}$

$\Rightarrow - a b = (k - b) (a - h)$

$\Rightarrow - a b = k a - k h - a b + b h$

$\Rightarrow k a + b h = k h$

Dividing both sides by kh we get,

$\Rightarrow \frac{k a}{k h} + \frac{b h}{k h} = \frac{k h}{k h}$

$\Rightarrow \frac{a}{h} + \frac{b}{k} = 1$

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13. If three points (h, 0), (a, b) and (0, k) lie on a line, show that $\frac{a}{h} + \frac{b}{k} = 1$ .