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The length of perpendicular from the origin to a line is 5 units and the line makes an angle 120° with the positive direction of x-axis.The equation of the line is
- a)x +√3y = 5
- b)√3x +y = 10
- c)√3x - y = 10
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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The length of perpendicular from the origin to a line is 5 units and t...
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The length of perpendicular from the origin to a line is 5 units and t...
To find the length of the line, we need to use trigonometry.
Let's assume that the line intersects the x-axis at point A and the y-axis at point B. The perpendicular from the origin to the line intersects the line at point C.
Since the length of the perpendicular from the origin to the line is 5 units, we can label the length of segment OC as 5.
We know that angle BOC is 120 degrees. Since OC is the hypotenuse, we can use the cosine function to find the length of segment BC.
cos(120) = BC/OC
cos(120) = BC/5
To find the length of BC, we can rearrange the equation:
BC = 5 * cos(120)
Using the unit circle, we know that cos(120) = -1/2. Therefore:
BC = 5 * (-1/2)
BC = -5/2
Since the distance cannot be negative, we take the absolute value of BC:
|BC| = 5/2
Therefore, the length of the line is 5/2 units.
Let's assume that the line intersects the x-axis at point A and the y-axis at point B. The perpendicular from the origin to the line intersects the line at point C.
Since the length of the perpendicular from the origin to the line is 5 units, we can label the length of segment OC as 5.
We know that angle BOC is 120 degrees. Since OC is the hypotenuse, we can use the cosine function to find the length of segment BC.
cos(120) = BC/OC
cos(120) = BC/5
To find the length of BC, we can rearrange the equation:
BC = 5 * cos(120)
Using the unit circle, we know that cos(120) = -1/2. Therefore:
BC = 5 * (-1/2)
BC = -5/2
Since the distance cannot be negative, we take the absolute value of BC:
|BC| = 5/2
Therefore, the length of the line is 5/2 units.
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