If three points h - 0- a - b and 0- k lies on a line- show that a - h - b - k -1

Let A(h, 0), B(a, b) and C(0, k) be three points lie on a line. ∴ Slope of AB = b 0/a h = b/a h Slope of BC = k b/0 a = b k/a Slope of AB = Slope of BC (gi ...

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Standard X

Mathematics

Point-Slope Form

If three poin...

Question

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

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Solution

Let A(h, 0), B(a, b) and C(0, k) be three points lie on a line.

$∴$ Slope of $A B = \frac{b - 0}{a - h} = \frac{b}{a - h}$

Slope of $B C = \frac{k - b}{0 - a} = \frac{b - k}{a}$

Slope of AB = Slope of BC (given)

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

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

Dividing both sides by hk

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

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If three points (h, 0), (a, b) and (0, k) lies on a line, show that ah+bk=1

Let A(h, 0), B(a, b) and C(0, k) be three points lie on a line. ∴ Slope of AB=b−0a−h=ba−h Slope of BC=k−b0−a=b−ka Slope of AB = Slope of BC (given) ∴ ba−h=b−ka⇒ab=ab−ak−bh+hk ⇒ ak+bh=hk Dividing both sides by hk akhk+bhhk=1 ⇒ ah+bk=1

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