Can you do all of the questions and plot them in a graph 

Here are the results based on the analysis and graph plotting:

1. **Gradient of Line AB:**
   - The gradient (slope) of the line connecting points A \((2, 3)\) and B \((5, 8)\) is approximately \(1.67\).

2. **Midpoint of Line PQ:**
   - The midpoint between points P \((3, 6)\) and Q \((9, 2)\) is \((6.0, 4.0)\).

3. **Distance Between Points P and Q:**
   - The distance between points P and Q is approximately \(7.21\) units.

In the graph, you can see the following:
- Points A, B, C, and D plotted in blue.
- Points P and Q plotted in red.
- Line AB (blue dashed) with its calculated gradient.
- Line PQ (red dashed) with the midpoint and distance shown.

### Follow-Up Questions

1. How would the graph change if we rotated the points 90 degrees counterclockwise?
2. What would happen to the gradient if the coordinates of points A and B were swapped?
3. Can you find the equation of the line passing through points A and B?
4. How would the distance between P and Q change if both points were shifted up by 5 units?
5. What is the area of the triangle formed by points A, B, and C?

### Tip:
Always double-check your plotted points to ensure accuracy, especially when using them to calculate distances or gradients.

Explore coordinate geometry problems with detailed solutions and graph analysis. This page covers the gradient of lines, midpoints, and distances between points. Includes plotted graphs and follow-up questions for further exploration.

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