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Loci (Locus) | O Level Mathematics 4024 & IGCSE Mathematics 0580 | Detailed Free Notes To Score An A Star (A*)

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  • If you have to find the something at “x cm distance from a point” – also called equidistant from a point
    • Insert a pencil in the compass
    • Open it using the ruler to the same length
    • Put it on the point
    • Draw the angle inside the shape where the region must be for the same distance
  • If you have to find the angle bisector
    • Consider this image

  • Put the compass on one of the points market in red
  • Open it more than half the distant to the other red points
    • More than half the distance is required because otherwise the cross won’t form
  • Mark a small cross on the other side of A (A is already of the point)
  • Then keeping it opened at the same length, place the compass on the other rend point
    • DO NOT CHANGE HOW WIDE IT IS OPENED
  • Mark the cross
  • Draw the line from the A to the cross

  • For equidistant from two points
  • Do the same steps as mentioned above, but now make crosses on both sides
  • See images below
    • All other rules same about compass opening etc

  • Do not lift the compass before making the mark on both sides of the line.

  • Remember, it is perpendicular bisector which means the angle is 90 and it divides the the line in two equal parts.

Equidistant from a line

  • Remember, a line is infinite, it has no end. A line segment has ends.
  • If you get a question regarding equidistant from a line/ line segment, the first steps are the same. It would have given you a distance that has to be taken. Use your ruler at various distances to mark the point on both sides of the line/ line segment. Then join the points with a straight line on both sides.

  • Now if this is a line segment, instead of a line, there is one extra step – you need to close the two sides as well.
  • Open your compass by the given distance (5 cm in this case).
  • Put it on one end of the segment and draw a semicircle that joins the line above and below it. Then do the same on the other end.

Hunain Zia

Hunain Zia has previously achieved considerable success in the high-school educational stream, gaining a massive 154 Total A Grades and 7 Major Distinctions, a process in which he broke/ set 11 different world records, including the most A grades ever achieved, most subjects ever appeared in, most distinctions, gaining distinctions across two separate boards (Pearson Edexcel and CAIE) within the same year/ ever, and even 19 hours of constant examination. All records stand intact today. Hunain pursued his Honors Accounting Degree from the prestigious Bentley University, and then completed an LLB (in Honors) from University of London. Currently, he manages multiple social and commercial projects, has founded digital streams and works tirelessly in the education sector.

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