Answer:
:To find the coordinates of point P along the directed line segment CD from C(8,4) to D(-10,-9), we can use the concept of partitioning the line segment in a given ratio.
First, let's calculate the distance between points C and D using the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance = sqrt((-10 - 8)^2 + (-9 - 4)^2)
Distance = sqrt((-18)^2 + (-13)^2)
Distance = sqrt(324 + 169)
Distance = sqrt(493)
Distance ≈ 22.203
Now, we need to determine the coordinates of point P, which partitions the line segment CD in the ratio of 1 to 5.
Let's assume that the coordinates of point P are (x, y).
To calculate the position of point P, we can use the section formula:
x = ((5 * x2) + (1 * x1)) / (5 + 1)
y = ((5 * y2) + (1 * y1)) / (5 + 1)
Substituting the known values:
x = ((5 * -10) + (1 * 8)) / 6
y = ((5 * -9) + (1 * 4)) / 6
Simplifying:
x = (-50 + 8) / 6
y = (-45 + 4) / 6
x = -42 / 6
y = -41 / 6
x ≈ -7
y ≈ -6.833