Let's solve this step-by-step.
1. Identify the given points:
- Point [tex]\( A \)[/tex] is at [tex]\(-3\)[/tex]
- Point [tex]\( C \)[/tex] is at [tex]\(-1\)[/tex]
2. Given ratio:
- The ratio [tex]\( CB:BA \)[/tex] is 1:3
3. Calculate the total parts in the ratio:
- Total parts = [tex]\( 1 + 3 = 4 \)[/tex]
4. Calculate the distance between [tex]\( A \)[/tex] and [tex]\( C \)[/tex]:
- Distance [tex]\( AC = C - A = -1 - (-3) = -1 + 3 = 2 \)[/tex]
5. Calculate the length of each part:
- Each part's length = [tex]\( \frac{Distance \, AC}{Total \, parts} = \frac{2}{4} = 0.5 \)[/tex]
6. Find the location of [tex]\( B \)[/tex]:
- [tex]\( CB = 1 \)[/tex] part, therefore distance [tex]\( CB = 1 \times 0.5 = 0.5 \)[/tex]
- Since [tex]\( C \)[/tex] is at [tex]\(-1\)[/tex] and [tex]\( CB = 0.5 \)[/tex], moving 0.5 units to the left from [tex]\( C \)[/tex] will give us the location of [tex]\( B \)[/tex]
- Location of [tex]\( B = C - 0.5 = -1 - 0.5 = -1.5 \)[/tex]
So, the location of point [tex]\( B \)[/tex] is [tex]\(-1.5\)[/tex].
The correct answer is:
-1.5
