Q&A for How to Construct a Perpendicular Line to a Given Line Through Point on the Line

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  • Question
    How do I find the equation of the line?
    Kevin Wang
    Kevin Wang
    Math Tutor
    Kevin Wang is a Math Tutor based in New York, New York. Kevin has been tutoring math for over 10 years, and specializes in K-12 math topics and standardized tests, such as SAT and ACT. Kevin has an economics background and a career in both finance and marketing analytics. His interest in tutoring goes back even longer than his career. He discovered tutoring at the start of his university career and enjoys it as a way to stay sharp with fundamental skills and remain up to date with trends in our education system. Kevin received a BS in Economics from Duke University.
    Kevin Wang
    Math Tutor
    Expert Answer
    To find a line perpendicular to another line, two things must be done: first, flip the slope of the other line upside down and change its sign. For example, if it is 2, the slope of a perpendicular line would be -1/2. Second, pick a point that the new line goes through. Once you have the slope and have a point, you can now use the point formula to find the equation of the perpendicular line.
  • Question
    Can we draw the arc both above/below the line?
    Donagan
    Donagan
    Top Answerer
    Yes. With either of the methods shown above, you may (but don't have to) draw similar arcs on both sides of the given line. An arc (or arcs) on just one side of the line is sufficient, but drawing them on both sides is a good way to verify the accuracy of the perpendicular line.
  • Question
    How can I divide a straight line into 6 equal parts?
    Donagan
    Donagan
    Top Answerer
    Assuming no measuring tool or protractor, this can be done with a compass and straightedge. Label the line AB. From A draw another straight line at any acute angle from AB. Mark off six equal segments on this new line. Label the segments AC, CD, DE, EF, FG and GH. Draw a line from H to B. From line AH draw five lines to AB that are each parallel to HB. (Use a compass or protractor to make these lines parallel to HB.) These parallel lines will intersect AB so as to divide AB into six equal parts.
  • Question
    What if the point is already drawn?
    Donagan
    Donagan
    Top Answerer
    Use that point as "the given point" in either of the above methods.
  • Question
    How many perpendicular can be drawn at a particular point on a straight line?
    Community Answer
    Community Answer
    Only one line can be drawn perpendicular to a straight line at any given point on that line.
  • Question
    How can you draw a perpendicular line a then make a line parallel to it?
    Community Answer
    Community Answer
    Two ways: (1) Pick a different point on the line, and draw a perpendicular line through that point; (2) Simply draw a line parallel to the first perpendicular line.
  • Question
    How to draw perpendicular bisector?
    Donagan
    Donagan
    Top Answerer
  • Question
    How to construct inscribed equilateral triangle?
    Donagan
    Donagan
    Top Answerer
    If you want to inscribe an equilateral triangle inside a circle, you can do it with a protractor and a drawing compass. Draw a circle with the compass, and note the circle's center. At the center, divide the circle into three 60° angles, and note the three points where the radii meet the circumference. Join those three points with straight lines, and you have drawn an inscribed equilateral triangle.
  • Question
    How is a perpendicular line through a point on a line similiar to a perendicular line through a point off a line?
    Donagan
    Donagan
    Top Answerer
    Actually, the two are identical. They look exactly the same. A perpendicular line passing through a point on another line passes through an infinite number of points off that line.
  • Question
    How can I draw a line and then add three more lines perpendicular to it?
    Donagan
    Donagan
    Top Answerer
    Select any three points on the original line. Then, for each point, use one of the methods described in the above article.
  • Question
    How can I draw a perpendicular line through a point on a line using only a ruler?
    Donagan
    Donagan
    Top Answerer
    You can't do it accurately with just a ruler. It's better to use a protractor, drafting compass, or drafting triangle. You can attempt it by using the ruler as a makeshift compass, but it's not recommended for precision.
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