Final answer:
To find the coordinates of point P along the directed line segment AB so that AP to PB is in the ratio 3 to 1, we use the section formula. Substituting the values into the formula, we find that the coordinates of point P are (-1, -2).
Step-by-step explanation:
To find the coordinates of point P along the directed line segment AB so that AP to PB is in the ratio 3 to 1, we can use the concept of section formula.
The section formula states that if we have two points A(x1, y1) and B(x2, y2), and we want to find a point P along the line segment AB such that AP to PB is in the ratio m to n, then the coordinates of P can be found using the following formulas:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
In this case, A(-4, -8) and B(0, 0).
Let's substitute the values into the formula:
x = (3 * 0 + 1 * -4) / (3 + 1) = -4/4 = -1
y = (3 * 0 + 1 * -8) / (3 + 1) = -8/4 = -2
Therefore, the coordinates of point P are (-1, -2).