https://file.aiquickdraw.com/mathbot/file/1728511842420ymluy2bc.jpg

Let's analyze the problem:

### Part a) 
You are asked to find the region that satisfies:
- **less than 3 cm from point P** and 
- **less than 4 cm from point Q**.

This is the intersection of two circles:
- A circle of radius 3 cm centered at P, and 
- A circle of radius 4 cm centered at Q.

For the region that is *less than 3 cm from P* and *less than 4 cm from Q*, it must be the common area inside both circles.

**Correct answer for a) is Diagram C** because the shaded region shows the area where the circles overlap, satisfying both conditions (inside both circles).

---

### Part b) 
You are asked to find the region that satisfies:
- **more than 3 cm from point P** and 
- **less than 4 cm from point Q**.

This is a region:
- Outside the 3 cm circle centered at P, and 
- Inside the 4 cm circle centered at Q.

**Correct answer for b) is Diagram F** because the shaded region is outside the 3 cm circle but still inside the 4 cm circle.

---

Would you like a further breakdown of these concepts or have any other questions?

### 5 Related Questions:
1. What is a locus of points, and how is it used in geometry?
2. How do you find the intersection of two circles geometrically?
3. Can we generalize the distance between points in a coordinate plane using this method?
4. How would the solution change if the distances were different, say 5 cm and 6 cm?
5. What is the formula to find the equation of a circle given a center and a radius?

### Tip:
When solving locus problems involving distance, always visualize the circles and look for common regions that meet the conditions specified.

Which of these diagrams shows the locus of points that are less than 3 cm from P and less than 4 cm from Q? And more than 3 cm from P and less than 4 cm from Q?

This problem explores the concept of loci and the intersection of circles, finding the regions that satisfy specific distance conditions from points P and Q. Ideal for students in Grades 8-10, it covers circle equations and theorems about the locus of points.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation