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.