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Collinear Points

Prove that th...

Question

Prove that the points $(- a, - b), (0, 0), (a, b)$ and $(a^{2}, a b)$ are collinear.

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Solution

As per slope formula:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

As per given points

Slope of AB = $\frac{0 - (- b)}{0 - (- a)}$

$= \frac{b}{a}$

Slope of CD = $\frac{b (a - 1)}{a (a - 1)}$

$= \frac{b}{a}$

Slope AB and slpoe of CD $= \frac{b}{a}$

$∴$ points A,B,C & D are colinear.

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Similar questions

a \neq b \neq 0

, prove that the points

(a, a^{2}), (b, b^{2})

(0, 0)

will not be collinear.

(a, 0), (0, b)

(x, y)

are collinear, prove that

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

The points (-a, -b), (0, 0), (a, b) and ( $a^{2}$ , ab) are

(a, 0), (0, b)

(1, 1)

are collinear, then

(\frac{a + b}{a b})

(- a, - b), (0, 0), (a, b)

(a^{2}, a b)

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