Question

What are the coordinates of the point on the directed line segment from

(-3Ė-5) to (9Ė-8) that partitions the segment into a ratio of 2 to 1?
Answer Attempt 1 out of 2
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Answer 1

To find the coordinates of the point that partitions the directed line segment from (-3, -5) to (9, -8) into a ratio of 2 to 1, you can use the following formula:

The coordinates of the point (x, y) can be found using the ratio k:

x = ((1 - k) * x1) + (k * x2)
y = ((1 - k) * y1) + (k * y2)

In this case, x1 = -3, y1 = -5, x2 = 9, y2 = -8, and you want the ratio to be 2 to 1, so k = 2/3 (because 2/(2+1) = 2/3).

Now, plug these values into the formulas:

x = ((1 - 2/3) * (-3)) + ((2/3) * 9)
x = (-1/3 * (-3)) + (18/3)
x = 1 + 18/3
x = 1 + 6
x = 7

y = ((1 - 2/3) * (-5)) + ((2/3) * (-8))
y = (-1/3 * (-5)) + (-16/3)
y = 5/3 - 16/3
y = -11/3

So, the coordinates of the point that partitions the segment into a ratio of 2 to 1 are (7, -11/3).