To calculate the area of the triangle, we use the formula for the area of a right triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

From the diagram:

1. The base of the triangle lies along the $x$-axis, extending from $x = 1$ to $x = 7$, so the base length is: $\text{base} = 7 - 1 = 6$

2. The height of the triangle is the vertical distance from the point $(6, 8)$ to the base, which is the $y$-coordinate difference: $\text{height} = 8 - 3 = 5$

Now, substituting into the formula: $\text{Area} = \frac{1}{2} \times 6 \times 5 = 15$

Final Answer:

The area of the triangle is 15 square units.

Would you like a more detailed explanation or assistance with related problems?

Related Questions:

1. How is the area formula derived for different types of triangles?
2. How can we determine the height if it isn't directly given?
3. Can the area of a triangle be found using vector methods?
4. What other methods can be used to calculate the area of triangles in coordinate geometry?
5. How do we verify if a triangle is a right triangle given three points?

Tip:

For triangles in coordinate geometry, double-check the base and height measurements