Question 1: Construct the locus of points equidistant from points A and B, where A is at (2, 3) and B is at (6, 7).

Answer: The perpendicular bisector of AB

Question 2: Plot the locus of points that are 4 units from the point (5, 5).

Answer: A circle with radius 4 centered at (5,5)

Question 3: Construct the locus of points equidistant from a line and a point not on the line.

Answer: The locus is the parabola with the focus at the point and directrix perpendicular to the line

Question 4: Plot the locus of points that are 3 units from the line y=2.

Answer: Two parallel lines y=5 and y=-1

Question 1: A point P moves such that it is always equidistant from points A(1, 2) and B(5, 6). A student claims the locus is a circle. Explain whether this is correct and justify your answer.

Answer: Incorrect; the locus is the perpendicular bisector of AB, which is a straight line, not a circle.

Question 2: Construct the locus of points that are both 5 units from point C(4, 4) and 3 units from line y=1. Describe the shape of this locus.

Answer: The locus is the intersection of a circle centered at C with radius 5 and two lines parallel to y=1 at distance 3, forming two circles and two lines.

Question 3: Explain how the locus of points equidistant from two intersecting lines is constructed.

Answer: The locus is the angle bisectors of the intersecting lines.

Question 1: A surveyor is marking out a region that is exactly 10 meters from a river represented by the line y=0. If they want to mark a point 15 meters from a village at (8, 12), how should they proceed?

Answer: Construct a circle of radius 10 around the river line and find the intersection points with a circle of radius 15 centered at the village.

Question 2: A drone needs to fly such that it remains equidistant from two landmarks at (3, 4) and (7, 8). Describe the path it should follow.

Answer: The drone should fly along the perpendicular bisector of the segment connecting the two landmarks.

Question 1: Construct the locus of points that are simultaneously 5 units from circle A with radius 3 and 7 units from circle B with radius 4, where the circles intersect. Describe the shape formed.

Answer: The locus forms two circles or arcs resulting from the intersection of the given loci, forming an almond-shaped shape (vesica piscis).

Question 2: Given two lines that intersect at (2, 3), construct the locus of points equidistant from both lines. Explain any special features of this locus.

Answer: The locus is the angle bisectors of the intersecting lines, possibly two lines dividing the angles.

Question 1: A student claims that the locus of points equidistant from two parallel lines is a single point. Is this correct? Explain and correct the misconception.

Answer: Incorrect; the locus is the line exactly midway between the two lines, not a point.

Question 2: Identify the mistake in this reasoning: 'The locus of points 4 units from a circle is another circle with radius 4.'

Answer: Incorrect; the locus is a pair of concentric circles or arcs, depending on the position, not necessarily another circle.