Question

Question 4(Multiple Choice Worth 1 points)

(04.03 MC)
On a number line, point A is located at 4, point C is located at 11, and point B lies between points A and C. What is the location of B such that the ratio of AB BC is 2:3

8.2
6.8
5.9
5.6

Answer 1

The location of point B on the number line is at 6.8 to maintain the ratio of AB to BC as 2:3.

Step-by-step explanation:

We are given three points A, B, and C on a number line with A at 4, B between A and C, and C at 11. We need to find the position of B such that the ratio of AB to BC is 2:3. To solve this, we can set up the ratio as a proportion: AB/BC = 2/3.

Let x represent the position of B. So, AB is (x - 4) and BC is (11 - x). Now we can write our proportion as (x - 4)/(11 - x) = 2/3. Cross-multiplying gives us 3(x - 4) = 2(11 - x).

Expanding both sides, we get 3x - 12 = 22 - 2x. Combining like terms, 3x + 2x = 22 + 12 leads to 5x = 34. Finally, dividing by 5 gives us x = 34/5 or x = 6.8.

Therefore, the location of point B is at 6.8 on the number line.