WEBVTT 00:00:00.500 --> 00:00:03.868 Welcome to GCSE Edexcel Maths revision. 00:00:04.018 --> 00:00:07.871 Topic M 28: Constructions, loci and bearings. 00:00:08.021 --> 00:00:10.816 This video covers Foundation and Higher tiers. 00:00:13.467 --> 00:00:17.828 For a construction, use a ruler for straight lines and a compass for arcs. 00:00:17.978 --> 00:00:25.219 Leave construction arcs visible; a protractor drawing is not a substitute when ruler-and-compass construction is required. 00:00:27.900 --> 00:00:33.477 To bisect a segment A B, use an equal compass radius greater than half A B from A and B. 00:00:33.627 --> 00:00:40.783 Join the two arc intersections: this perpendicular bisector is at 90 degrees to A B and passes through its midpoint. 00:00:40.933 --> 00:00:43.557 Constructing a perpendicular bisector 00:00:48.233 --> 00:00:52.363 To bisect an angle, draw an arc from the vertex crossing both arms. 00:00:52.513 --> 00:00:59.145 From those two crossings draw equal-radius arcs that meet inside the angle; join their intersection to the vertex. 00:01:01.800 --> 00:01:08.155 To construct a perpendicular from a point on a line, mark equal distances on the line on either side of the point. 00:01:08.305 --> 00:01:10.864 Construct their perpendicular bisector. 00:01:13.533 --> 00:01:21.915 To construct a perpendicular from a point off a line, draw an arc from the point crossing the line twice, then bisect the segment between those crossings. 00:01:22.065 --> 00:01:24.689 The result passes through the original point. 00:01:27.367 --> 00:01:32.015 The shortest distance from a point to a line is measured perpendicular to the line. 00:01:32.165 --> 00:01:34.256 A sloping connection is longer. 00:01:36.933 --> 00:01:39.865 A locus is the set of points meeting a condition. 00:01:40.015 --> 00:01:47.481 Points a fixed distance from one point form a circle; points equidistant from A and B lie on the perpendicular bisector of A B. 00:01:50.133 --> 00:01:54.910 Points equidistant from two intersecting lines lie on their angle bisectors. 00:01:55.060 --> 00:02:00.253 Points a fixed distance from a straight line lie on two parallel lines, one on each side. 00:02:02.933 --> 00:02:09.951 For within 3 centimetres of A, include the circular region of radius 3 centimetres, not just its circumference. 00:02:10.101 --> 00:02:15.155 For more than 3 centimetres away, use the outside region with the boundary excluded. 00:02:17.833 --> 00:02:20.765 Combine conditions by taking their intersection. 00:02:20.915 --> 00:02:28.935 A point within 4 centimetres of A and closer to B than C must lie in the overlap of the circle region and the appropriate half-plane. 00:02:31.600 --> 00:02:39.555 Use solid boundaries for at most or at least when equality is allowed; make excluded boundaries clear if the question uses strict inequalities. 00:02:42.233 --> 00:02:52.417 A bearing is measured clockwise from north and written with three digits: east is zero nine zero degrees, south one eight zero degrees and west two seven zero degrees. 00:02:52.567 --> 00:02:54.850 Draw a north line at the starting point. 00:02:55.000 --> 00:02:57.539 A bearing of one hundred twenty degrees 00:03:02.200 --> 00:03:10.582 For a reverse bearing, add or subtract one eight zero degrees and keep the result from zero zero zero degrees to three five nine degrees. 00:03:10.732 --> 00:03:16.342 A bearing of B from A of zero six five degrees gives A from B as two four five degrees. 00:03:19.000 --> 00:03:23.203 Worked example: At scale 1 centimetre represents 2 kilometres, 00:03:23.353 --> 00:03:32.078 a 7 kilometres journey on bearing one two zero degrees is drawn as a 3.5 centimetres line clockwise one two zero degrees from north. 00:03:32.228 --> 00:03:34.489 The bearing's starting point matters. 00:03:37.167 --> 00:03:43.000 When several bearings are given, use parallel north lines and angle rules to find triangle angles. 00:03:43.150 --> 00:03:47.380 Do not treat the bearing as automatically an interior angle of the triangle. 00:03:50.033 --> 00:03:53.089 That completes Constructions, loci and bearings. 00:03:53.239 --> 00:03:56.584 Revisit the notes and test yourself on the revision website.