To find the coordinates of point $P$, which is the weighted average of points $A(7, 3)$ and $B(-3, -10)$, with point $A$ weighing three times as much as point $B$, we use the formula for the weighted average of two points:

$P = \left( \frac{m_A \cdot x_A + m_B \cdot x_B}{m_A + m_B}, \frac{m_A \cdot y_A + m_B \cdot y_B}{m_A + m_B} \right)$

Here, $m_A = 3$ and $m_B = 1$, since point $A$ weighs three times as much as point $B$.

Let's calculate the coordinates of $P$:

1. x-coordinate of P:

$x_P = \frac{3 \cdot 7 + 1 \cdot (-3)}{3 + 1} = \frac{21 - 3}{4} = \frac{18}{4} = \frac{9}{2}$

2. y-coordinate of P:

$y_P = \frac{3 \cdot 3 + 1 \cdot (-10)}{3 + 1} = \frac{9 - 10}{4} = \frac{-1}{4}$

So, the coordinates of point $P$ are $\left( \frac{9}{2}, -\frac{1}{4} \right)$.

The correct answer is:

C) $\left(\frac{9}{2}, -\frac{1}{4}\right)$

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Would you like further details or have any questions? Here are five related questions:

1. How do you find the midpoint of two points?
2. What is the general formula for the weighted average of three points?
3. How can we find the centroid of a triangle given its vertices?
4. What is the significance of the weights in calculating the weighted average?
5. How do you apply the distance formula between two points?

Tip: Always double-check your calculations when dealing with fractions to avoid simple arithmetic errors.