To find the coordinates of the intersection of the diagonals of a parallelogram, we can use the midpoint formula. In a parallelogram, the diagonals bisect each other, so the intersection point will be the midpoint of the line segment formed by connecting opposite vertices.

Here’s how to find it:

1. Identify Opposite Vertices: In this case, we can consider $A(8,6)$ and $C(16,4)$ as one pair of opposite vertices, and $B(14,8)$ and $D(10,2)$ as the other pair.

2. Calculate the Midpoint of Diagonal $AC$: $\text{Midpoint} = \left( \frac{8 + 16}{2}, \frac{6 + 4}{2} \right) = \left( \frac{24}{2}, \frac{10}{2} \right) = (12, 5)$

3. Calculate the Midpoint of Diagonal $BD$ (just to verify, though it should be the same since it’s a parallelogram): $\text{Midpoint} = \left( \frac{14 + 10}{2}, \frac{8 + 2}{2} \right) = \left( \frac{24}{2}, \frac{10}{2} \right) = (12, 5)$

Thus, the coordinates of the intersection of the diagonals are $(12, 5)$.

Would you like more details on the steps?

Here are five related questions to explore further:

1. How do you find the midpoint if the coordinates include fractions or decimals?
2. What other properties of parallelograms can be proven using the diagonal intersection point?
3. How would the method change if this were a trapezoid instead of a parallelogram?
4. Can the midpoint formula be applied in three-dimensional geometry for a parallelogram?
5. How can we verify if given four points form a parallelogram?

Tip: Remember, the diagonals of a parallelogram always bisect each other, so finding their midpoint directly gives you the intersection point!