Final answer:
The coordinate of point F, which is 1/3 of the way from D to C on a number line, can be found by determining 1/3 of the distance between D and C and subtracting it from D's coordinate. The coordinate of F is 13 2/3.
Step-by-step explanation:
To find the coordinate of point F which is 1/3 of the way from point D to point C on a number line, we can use the concept of finding a point on a line segment. Given that point C is at -5 and point D is at 23, the total distance between C and D is 23 - (-5) = 28 units.
To find a point that is 1/3 of the way from D towards C, we multiply the total distance by 1/3:
1/3 of the way = 1/3 × 28 units = 28/3 units = 91/3 units.
Since F is 1/3 of the way from D towards C, we need to subtract this distance from D's coordinate:
F's coordinate = D's coordinate - (1/3 of the way)
F's coordinate = 23 - 91/3 = 13 2/3
Therefore, the coordinate of F is 13 2/3.