OCR GCSE MATHS 6.3 AND 6.4 LOCI AND PROBLEMS(Construction and loci) QUESTIONS AND CORRECT ANSWERS GRADED A+

6.3 AND 6.4 LOCI AND PROBLEMS ©Cambridge University Press and OCR 2021 2 2 The locus of all points that are equidistant from two lines will bisect the angle between the two lines. AB and BC represent the sides of a field. Jack is in the corner of the field at point B. He wants to walk into the field in a straight line, so that he is always equidistant from the sides AB and BC. Draw and describe the locus of the path he must take. • Draw the angle bisector of ∠ABC. For the method see sheet 6.1 and 6.2. The locus is described as the angle bisector of ∠ABC (marked as line BP on the diagram). 3 The locus of points equidistant from a line segment. Clara runs so that she is always a fixed distance from a straight railway line. Draw and describe the locus of her run. • Using a ruler, draw lines that are parallel to the railway line. The locus is described as a pair of parallel lines that are equidistant from the railway line. If the railway line had a fixed length AB, then the locus would look like below, because she could be a fixed distance from the ends of the line (A and B) as well. You would draw the semi-circular ends with compasses with the point on A and then B. 4 The locus of all points that are equidistant from two points A and B form the perpendicular bisector of the line AB. Alex lives at point A and Beth lives at point B. They want to meet anywhere that is an equal distance between their homes. Draw and describe the locus of all possible meeting places. • Using compasses, draw the perpendicular bisector of line AB. For the method see sheet 6.1 and 6.2. The locus is any point along the perpendicular bisector of AB. 6.3 AND 6.4 LOCI AND PROBLEMS ©Cambridge University Press and OCR 2021 3 6.4 Loci problems Exercise 1 1 Without drawing them, describe the point, path or area that each locus below will produce. a Points that are 200km from point X. b Points that are equidistant from the four corners of a rectangle. c Points that are within 1km of a straight railway line. 2 Accurately construct the locus of points 4cm from a point O. 3 Draw ∠MNR = 50°. Accurately construct the locus of points equidistant from MN and NR. 4 Draw line PQ that is 4cm long. Using a ruler and compasses, construct the locus of points 1cm from PQ. 5 Draw a rectangle ABCD with AB = 6cm and BC = 4cm. a Construct the locus of points that are equidistant from AB and BC. b Shade the locus of points that are less than 1cm from the centre of the rectangle. c Construct the locus of points that are exactly 1cm outside the perimeter of the rectangle. 6 In this question, use ruler and compasses only and show your construction lines clearly. ABC is a field. A wind turbine is to be erected in the field. The turbine must be the same distance from A as it is from B. The turbine must also be equidistant from AB and BC. Mark on your diagram with a letter W, the place where the turbine needs to be erected.