Question

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?

Answer 1

Answer:

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: $\frac{bx_1+ax_2}{a+b}$ and

y coordinate: $\frac{by_1+ay_2}{a+b}$

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

$\frac{4(-9)+3(-2)}{7}$ which simplifies down to -6, and

the y coordinate of the directed point is

$\frac{4(-7)+3(7)}{7}$ which simplifies down to -1.

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

Answer 2

Answer:

(-6, -1)

Step-by-step explanation:

It's right