Question

1. choose the best answer. using the given coordinates and the ruler postulate, calculate the length of the line segment. (overline{df}) image: a line ( ell ) with points a, b, c, d, e, f, g, h, i, j, k, and a ruler below marked from 0 to 6 (with 1, 2, 3, 4, 5, 6 labeled). options: 1, 3, ( \frac{2}{3} ), -1

Explanation:

Step1: Identify coordinates of D and F

From the ruler, D is at 2, F is at 3.

Step2: Apply Ruler Postulate

Length of \(\overline{DF}\) is \(|3 - 2| = 1\)? Wait, no, wait. Wait, looking at the ruler, maybe the scale: Let's check the positions. Wait, B is at 1, C between 1 and 2, D at 2, E between 2 and 3, F at 3? Wait, no, maybe the distance between D and F: Let's count the units. Wait, D is at 2, F is at 3? No, wait, maybe the coordinates: Wait, the ruler has marks. Wait, D is at 2, F is at 3? Then \(|3 - 2| = 1\)? But wait, maybe the scale is different. Wait, no, let's re-examine. Wait, the line segment DF: D is at 2, F is at 3? Wait, no, maybe the coordinates are such that D is at 2, F is at 3? Wait, no, maybe the distance is 1? Wait, but the options have 1, 3, 2/3, -1. Wait, length can't be negative. So -1 is out. Let's check again. Wait, D is at 2, F is at 3? Then \(|3 - 2| = 1\). Wait, but maybe the ruler is marked with fractions. Wait, B is at 1, C is at 1.5? No, the ruler has marks from 1 to 6, with each major mark at 1, 2, 3, 4, 5, 6. Wait, D is at 2, F is at 3? Then the distance is 1. But wait, maybe I misread. Wait, D is at 2, E is at 2.5, F is at 3? Then DF is 3 - 2 = 1? Wait, no, maybe the coordinates: Let's see, the ruler is below the line. The points: A, B, C, D, E, F, G, H, I, J, K. B is at 1, C at 1.5? No, the ruler has marks at 1, 2, 3, 4, 5, 6. So D is at 2, F is at 3? Then DF length is 3 - 2 = 1. So the answer is 1. Wait, but let's confirm the Ruler Postulate: The length of a segment is the absolute difference of its coordinates. So if D has coordinate 2 and F has coordinate 3, then length is |3 - 2| = 1.

Answer:

1 (corresponding to the first option, e.g., if the first option is "1", then the answer is the option with "1")