Which of the following line(s) would make a right-angled triangle with the coordinate axes?

3 x + 2 y = 6

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3 x + 2 y = - 6

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x - y = 1

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3 y = 15

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Solution

The correct options are
A $3 x + 2 y = 6$
B $3 x + 2 y = - 6$
C $x - y = 1$

Any line that isn't parallel to the coordinate axes and not passing through the origin will inevitably cut the two coordinate axes making a right angled triangle.

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Find the direction cosines of a line which makes an angle θ with all three the coordinate axes.

(a) \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} (b) \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}} (c) - \frac{1}{\sqrt{3}}, - \frac{1}{\sqrt{3}}, - \frac{1}{\sqrt{3}} (d) \pm \frac{1}{3}, \pm \frac{1}{3}, \pm \frac{1}{3}

a x + c y = 2 b

a, b, c > 0

2

(α, β, γ)

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