https://file.aiquickdraw.com/mathbot/file/1729534424594nxcxttsg.jpg

Let's go through each part of the question by analyzing the diagrams.

### a) **The locus of points that are less than 6 cm from Q:**
- This locus forms a circle with radius 6 cm around point Q.
- Diagram **D** shows a circle of radius 6 cm around Q, with the region inside this circle shaded. This matches the description.

### b) **The locus of points that are closer to P than to Q:**
- This is the perpendicular bisector of the line segment joining P and Q. The region closer to P will be on one side of this bisector.
- Diagram **F** shows a vertical line that divides the plane into two equal parts, shading the side closer to P. This matches the description.

### c) **The locus of points that are more than 6 cm from P:**
- This forms the region outside a circle of radius 6 cm centered at P.
- Diagram **A** shows the region outside a circle centered at P with a radius of 6 cm. This matches the description.

### Summary of correct diagrams:
- **a)** Diagram **D**.
- **b)** Diagram **F**.
- **c)** Diagram **A**.

Would you like further clarification on any of these? 

Here are 5 related questions to expand on this:
1. How do you find the equation of a circle given the center and radius?
2. What is the definition of a locus of points in geometry?
3. Can two loci ever overlap, and under what conditions would this happen?
4. How do you construct a perpendicular bisector for a line segment geometrically?
5. How does the distance formula relate to the locus of points equidistant from two points?

**Tip:** When solving locus problems, always think about distance and symmetry, especially when dealing with geometric figures like circles and lines.

In which of these diagrams does the shaded region show: a) the locus of points that are less than 6 cm from Q? b) the locus of points that are closer to P than to Q? c) the locus of points that are more than 6 cm from P?

Learn how to solve locus problems involving points less than or greater than a fixed distance from given points and regions closer to one point than another. This solution covers concepts of circles, perpendicular bisectors, and locus, ideal for students in Grades 9-11.

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