Question

Find the point, M, that divides segment AB into a ratio of 5:3 if A is at (-4, -2) and B is at (4, -10).

A) (1, -7)
B) (2, -7)
C) (2, -8)
D) (1, -8)

Answer 1

Now remember with this situation, 5:3 is not 5/3, but rather it's "5 equal parts to 3 equal parts", which is a total of 8 equal parts. This problem wants you to place point M at 5/8 the distance from A to B.

Firstly, how many units apart is -4 to 4 (the x-coordinates)? That's 8 units. Multiply 5/8 by 8:

`(5)/(8)*(8)/(1)=(40)/(8)=5`

Next, how many units apart is -2 to -10 (the y-coordinates)? That's 8 units as well. Multiply 5/8 by 8.

`(5)/(8)*(8)/(1)=(40)/(8)=5`

Now, since from -4 to 4 you are increasing, add 5 to -4:

`-4+5=1`

1 is your x-coordinate.

Now since from -2 to -10 you are decreasing, subtract 5 from -2:

`-2-5=-7`

-7 is your y-coordinate.

Putting it all together, point M is at (1,-7), or A.