Question
P, Q, R are three villages PQ=10 km , QR=8km and PR is 4km are connecting roads. Using a scale of one cm to represent one km ,locate the relative positions of the three villages
Answers
GPT-4o mini
To locate the relative positions of villages P, Q, and R, we can represent the distances on a piece of paper using the given scale of 1 cm = 1 km. The distances between the villages are:
- PQ = 10 km (10 cm)
- QR = 8 km (8 cm)
- PR = 4 km (4 cm)
Here’s how to plot the points step-by-step:
1. **Draw Line PQ**:
- Start by drawing a horizontal line segment representing PQ. Since PQ is 10 km, draw a line that is 10 cm long. Label the endpoints as P and Q.
2. **Locate Point R**:
- You know that PR = 4 km (4 cm) and QR = 8 km (8 cm). From point P, you will measure 4 cm towards the direction where R might be placed.
- From point Q, you will measure 8 cm in a suitable direction for point R.
3. **Finding R**:
- Since P and Q are fixed points, you can use the distances from both points to create circles where point R could be located.
- Draw a circle centered at P with a radius of 4 cm (this represents PR).
- Draw another circle centered at Q with a radius of 8 cm (this represents QR).
- The point where the two circles intersect is point R.
4. **Label the points**:
- After finding the intersection point, label it R.
You should find that R is positioned relative somewhere in the space according to the distances given. Make sure to maintain the correct scale and angles while drawing for accuracy.
### Summary of the steps:
- **Draw PQ (10 cm)**
- **Draw a circle at P (4 cm radius)**
- **Draw a circle at Q (8 cm radius)**
- **Intersecting point = R**
This will give you the relative positions of villages P, Q, and R on your paper.
- PQ = 10 km (10 cm)
- QR = 8 km (8 cm)
- PR = 4 km (4 cm)
Here’s how to plot the points step-by-step:
1. **Draw Line PQ**:
- Start by drawing a horizontal line segment representing PQ. Since PQ is 10 km, draw a line that is 10 cm long. Label the endpoints as P and Q.
2. **Locate Point R**:
- You know that PR = 4 km (4 cm) and QR = 8 km (8 cm). From point P, you will measure 4 cm towards the direction where R might be placed.
- From point Q, you will measure 8 cm in a suitable direction for point R.
3. **Finding R**:
- Since P and Q are fixed points, you can use the distances from both points to create circles where point R could be located.
- Draw a circle centered at P with a radius of 4 cm (this represents PR).
- Draw another circle centered at Q with a radius of 8 cm (this represents QR).
- The point where the two circles intersect is point R.
4. **Label the points**:
- After finding the intersection point, label it R.
You should find that R is positioned relative somewhere in the space according to the distances given. Make sure to maintain the correct scale and angles while drawing for accuracy.
### Summary of the steps:
- **Draw PQ (10 cm)**
- **Draw a circle at P (4 cm radius)**
- **Draw a circle at Q (8 cm radius)**
- **Intersecting point = R**
This will give you the relative positions of villages P, Q, and R on your paper.