The line, L1, makes an angle of 30° with the positive direction of the x-axis - Scottish Highers Maths - Question 7 - 2019
Question 7
The line, L1, makes an angle of 30° with the positive direction of the x-axis.
Find the equation of the line perpendicular to L1, passing through (0, –4),
Worked Solution & Example Answer:The line, L1, makes an angle of 30° with the positive direction of the x-axis - Scottish Highers Maths - Question 7 - 2019
Step 1
Find the gradient of L1
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Answer
The gradient (m) of the line L1 can be calculated using the tangent of the angle it makes with the x-axis:
m=tan(30°)=31
Step 2
Determine the gradient of the perpendicular line
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Answer
Since the lines are perpendicular, the gradient of the perpendicular line (m_perpendicular) can be found using the property of perpendicular lines:
mperpendicular=−m1=−3
Step 3
Determine the equation of the line
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Answer
Using the point-slope form of the line equation, where the line passes through the point (0, -4):
y−y1=m(x−x1)
Substituting the values:
y−(−4)=−3(x−0)
This simplifies to:
y+4=−3x
Therefore, the equation can be rearranged to:
y=−3x−4
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