What are the coordinates of the point on the directed line segment from (–9, -7) to (-2,7) that partitions the segment into a ratio of 3 to 4?

Step-by-step explanation:

Saving the long, drawn out derivation of the formulas to find the x and y coordinates of the directed point, suffice it to say that it is:

x coordinate: and

y coordinate:

where x1, x2, y1, and y2 are the coordinates from the given points and a and b are the numbers in the ratio, namely a = 3 and b = 4. Filling in accordingly:

the x coordinate of the directed point is

which simplifies down to -6, and

the y coordinate of the directed point is

which simplifies down to -1.

The coordinate of the point is (-6, -1). Write that down so you don't forget it.