Question

Refer to the number line. Find the coordinate of point X such that the ratio of BX to XF is 3:2.

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-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7

Answer 1

To find the coordinate of point X such that the ratio of BX to XF is 3:2, set up a proportion using the distances (x - b) / (f - x) = 3 / 2, where b and f are the coordinates of points B and F respectively. Solve this proportion for x after determining the positions of points B and F.

Step-by-step explanation:

To find the coordinate of point X such that the ratio of BX to XF is 3:2, we first need to identify the positions of points B and F on the number line. Let's assume point B is at the coordinate b and point F is at the coordinate f. The distance between B and F is f - b. According to the ratio 3:2, we can represent the total distance as 5 parts where 3 parts represent the distance from B to X and 2 parts represent the distance from X to F.

We can write a proportion to solve for the position of point X (let's call it x). The proportion is:

(x - b) / (f - x) = 3 / 2

This means that the distance from B to X is 3/5 of the total distance, and the distance from X to F is 2/5 of the total distance. Once we know the positions of points B and F, we can solve this proportion for x to find the coordinate of point X.

Without the actual positions of B and F, we cannot provide a numerical answer, but this is the strategy you would follow once those positions are known.