Answer:
To find the coordinate of point P, which represents the weighted average of points A and B, we need to consider the weights assigned to each point. Let's assume the coordinates of point A are (x₁, y₁), and the coordinates of point B are (x₂, y₂).
The weighted average formula for the x-coordinate of point P is:
xₚ = (w₁ * x₁ + w₂ * x₂) / (w₁ + w₂)
Similarly, the weighted average formula for the y-coordinate of point P is:
yₚ = (w₁ * y₁ + w₂ * y₂) / (w₁ + w₂)
In this case, the weight of point A is 2 and the weight of point B is 5. Plugging in the values, the formulas become:
xₚ = (2 * x₁ + 5 * x₂) / (2 + 5)
yₚ = (2 * y₁ + 5 * y₂) / (2 + 5)
Therefore, the coordinates of point P are given by:
P = ((2 * x₁ + 5 * x₂) / 7, (2 * y₁ + 5 * y₂) / 7)