If (a,b) (c,d) and (a-c, b-d) are collinear then

\frac{a}{b} = \frac{c}{d}

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\frac{a}{d} = \frac{b}{c}

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\frac{a}{c} = \frac{d}{b}

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\frac{a}{b} = \frac{b}{c}

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Solution

The correct option is A $\frac{a}{b} = \frac{c}{d}$
a(d - b + d) + c(b - d) + (a - c)(b - d)=0
or -2add - ab - cd+ ab - bc - ad + cd = 0
or ad - bc = 0 or ab=cd

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Similar questions

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 2 & a + b + c + d & a b + c d a + b + c + d & 2 (a + b) (c + d) & a b (c + d) + c d (a + b) a b + c d & a b (c + d) + c d (a + b) & 2 a b c d \end{matrix} ∣ ∣ ∣ ∣ ∣

a, b, c

d

x = \frac{a - b}{a + b + c + d} = \frac{b - c}{a + b + c + d} = \frac{c - d}{a + b + c + d} = \frac{d - a}{a + b + c + d}

x^{3}

Factorize $(a^{2} - b^{2}) (c^{2} - d^{2}) - 4 a b c d$

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