Question

Points A(−1.5) and B(6) are marked on a number line. Find the coordinate of point M if it is known that AM:MB=1:2. Find all possible answers.

Answer 1

suppose point M is at x
the length of AM is (x-(-1.5)), which is x+1.5
the length of MB is (6-x)
(x+1.5):(6-x)=1:2
2(x+1.5)=6-x
x=1
I cannot think of another possible answer unless M is NOT on the line.

Answer 2

M is at 1.

Explanation:

To solve this you just have to think a way to represent AM and MB in the equation we are about to do, the total of the segment is -1.5 to 6 and the units are 7.5, so the total segment measures 7.5 units, if AM is x then MB will be 2x. so our equation will look like this:

x+2x=7.5

3x=7.5

x=2.5 units

So x is 2.5 this means AM is 2.5 so point M is 2.5 away in the positive line from point A, -1.5+2-5=1

This means point M is located at 1 in the line.