Question 7 of 70intermediate🔧 ApplyShort Answer2 marks

Find the slope of the line, which makes an angle of 30∘30^\circ with the positive direction of yy-axis measured anticlockwise.

Correct Answer

The slope of the line is −3-\sqrt{3}.

Exercise: EXERCISE 9.1 | Q: 7 | (Page 8)
For More Understanding

Explanation

The question asks for the slope of a line making 30° with the positive y-axis measured anticlockwise. According to the textbook context, the inclination θ is defined as the angle made by a line with the positive direction of x-axis measured anticlockwise. The slope m = tan θ. Since the positive y-axis makes 90° with the positive x-axis, a line making 30° anticlockwise with the y-axis will make an angle of 90° + 30° = 120° with the positive x-axis. Therefore, θ = 120° and m = tan 120° = -3\sqrt{3}.

Solution Steps

  1. Step 1: The inclination θ is defined as the angle made by the line with the positive direction of x-axis measured anticlockwise.

  2. Step 2: The positive y-axis makes an angle of 90° with the positive x-axis.

  3. Step 3: Since the line makes 30° with the positive y-axis measured anticlockwise, the inclination θ = 90° + 30° = 120°.

  4. Step 4: By definition, slope m = tan θ = tan 120°.

  5. Step 5: Since tan 120° = tan(180° - 60°) = -tan 60° = -3\sqrt{3}, the slope is -3\sqrt{3}.

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