To determine which point is at the center of the four points $(6, 6)$, $(-10, 6)$, $(-10, -4)$, and $(6, -4)$, we calculate the midpoint of the diagonal pairs of the rectangle they form.

Step 1: Find the midpoint of the diagonals

The diagonals of a rectangle intersect at its center. The diagonal points can be paired as follows:

• Diagonal 1: $(6, 6)$ and $(-10, -4)$
• Diagonal 2: $(-10, 6)$ and $(6, -4)$

To find the midpoint of a diagonal, use the formula: $\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

Diagonal 1 Midpoint:

$\text{Midpoint} = \left( \frac{6 + (-10)}{2}, \frac{6 + (-4)}{2} \right) = \left( \frac{-4}{2}, \frac{2}{2} \right) = (-2, 1)$

Diagonal 2 Midpoint:

$\text{Midpoint} = \left( \frac{-10 + 6}{2}, \frac{6 + (-4)}{2} \right) = \left( \frac{-4}{2}, \frac{2}{2} \right) = (-2, 1)$

Step 2: Verify the midpoint

Both diagonals intersect at the same point, $(-2, 1)$.

Final Answer:

The point at the center is $\mathbf{B. \ (-2, 1)}$.

Would you like further details or explanations on how this calculation works?

Here are 5 related questions:

1. What is the formula to calculate the midpoint of a line segment?
2. How do you identify if four points form a rectangle on a coordinate grid?
3. What is the significance of the center point in a rectangle?
4. How do you find the distance between two points in a coordinate grid?
5. Can this method be used for polygons with more than four sides?

Tip: Always check whether the diagonals of a quadrilateral bisect each other equally to confirm it is a rectangle!