Question

The equation of the line having inclination 120°,
and dividing the join of (-1, 4) and (2, 6)
externally in the ratio 2 : 1, is
(x-5)/3 + y = 8
3.x + y = 13
x+y/3 = 8
none of these​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The equation of the line having inclination 120°, and dividing the join of (-1, 4) and (2, 6) externally in the ratio 2 : 1 is

$\displaystyle \sf{1. \: \: \: \: y + \sqrt{3} (x - 5) = 8}$

$\displaystyle \sf{2. \: \: \: \: \sqrt{3} x + y = 13}$

$\displaystyle \sf{3. \: \: \: \: x + y \sqrt{3} = 8}$

4. None of these

EVALUATION

Here it is given that the line divide the line joining the points (-1, 4) and (2, 6) externally in the ratio 2 : 1

So the point is

$\displaystyle \sf{ = \bigg( \: \frac{2 \times 2 - 1 \times ( - 1)}{2 - 1} \: , \: \: \frac{2 \times 6 - 1 \times 4}{2 - 1} \bigg)}$

$\displaystyle \sf{ = \bigg( \: \frac{4 + 1}{1} \: , \: \: \frac{12 - 4}{1} \bigg)}$

$\displaystyle \sf{ =( \: 5 \: , \: 8 )}$

Now the required line makes an inclination of 120°

Hence the required equation of the line is

$\displaystyle \sf{(y - 8) = \tan {120}^{ \circ} \times (x - 5)}$

$\displaystyle \sf{ \implies \: (y - 8) = - \cot {30}^{ \circ} \times (x - 5)}$

$\displaystyle \sf{ \implies \: (y - 8) = - \sqrt{3} \times (x - 5)}$

$\displaystyle \sf{ \implies \: y + \sqrt{3} (x - 5) = 8}$

FINAL ANSWER

Hence the correct option is

$\displaystyle \sf{1. \: \: \: \: y + \sqrt{3} (x - 5) = 8}$

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