Final answer:
The coordinates of the point that partitions the directed segment from A(-8, 4) to B(10, -2) in the ratio of 2:1 are (4, -0.67).
Step-by-step explanation:
To find the coordinates of the point that partitions the directed segment from A(-8, 4) to B(10, -2) in the ratio of 2:1, we can use the section formula. The section formula states that if we have two points (x1, y1) and (x2, y2), and we want to find the coordinates of a point P that divides the segment AB in the ratio m:n, then the coordinates of P can be found using the formulas:
x = ((n * x1) + (m * x2)) / (m + n)
y = ((n * y1) + (m * y2)) / (m + n)
Using this formula, we can substitute the given values:
x = ((1 * -8) + (2 * 10)) / (2 + 1) = 4
y = ((1 * 4) + (2 * -2)) / (2 + 1) = -0.67
Therefore, the coordinates of the point that partitions the directed segment from A(-8, 4) to B(10, -2) in the ratio of 2:1 are (4, -0.67).
Learn more about coordinates