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.

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !