Question

Find the coordinates of a point on the directed segment from (3,-2) to (8,0) that divides into a ratio of 3:1.

a. (6.75, -0.5)
b. (6, -.075)
c. (5, -1.5)
d. (4, -1.5)​

Answer 1

(x, y) = (6.75, -0.5)

Explanation:

You require the point (x, y) such that the distance from (3, -2) is 3 times the distance from (8, 0). That is ...

x-3 = 3(8 -x)

and

y-(-2) = 3(0 -y)

__

Solving the first equation, we get ...

x -3 = 24 -3x

4x = 27 . . . . . . . . . . . . add 3x+3

x = 27/4 = 6.75 . . . . . . this is sufficient to choose the correct answer.

__

Solving the second equation, we get ...

y +2 = -3y

4y +2 = 0 . . . . . add 3y

y + 1/2 = 0 . . . . . divide by 4

y = -0.5 . . . . . . . . . . . this confirms the correct answer choice.