Question

On a number line, point A is located at 0, point C is located at -2, and point B lies between points A and C. What is the location of B such that the ratio of CB:BA is 3:1?

Option 1: -1.5
Option 2: -0.5
Option 3: 0.67
Option 4: 1.5

Answer 1

Point B is located at -1.5 on the number line because this location maintains the ratio 3:1 for the lengths of segments CB to BA.

Step-by-step explanation:

The question involves finding point B on a number line such that the ratio of the lengths of segments CB to BA is 3:1, with point A at 0 and point C at -2. To find the location of point B, we consider that if the total distance from C to A is divided into four equal parts (since the ratio is 3:1), each part would be 0.5 units long because the distance from C to A is 2 units. Multiplying one part by 3 (because CB is three parts of the whole), we get that point B is 1.5 units to the left of A, meaning B is at -1.5.

Therefore, the location of point B is -1.5 on the number line, which corresponds to Option 1: -1.5.