Question

do you know how? find the length of each segment. number line with -5, 0, 5, points w, x, y 5. $overline{wx}$ 6. $overline{wy}$

Explanation:

Problem 5: Length of \(\overline{WX}\)

Step1: Determine positions of W and X

From the number line, the distance between -5 and 0 is 5 units, divided into 5 segments (since from -5 to 0 there are 5 intervals? Wait, looking at the number line: between -5 and 0, there are two marks: W and X. Wait, the number line has marks at -5, then W, then a mark, then X, then a mark, then 0. Wait, actually, let's count the units. The distance from -5 to 5 is 10 units, with 10 intervals (since from -5 to 5, there are 10 small segments? Wait, no, looking at the number line: from -5 to 0, there are 5 small segments? Wait, the points: -5, then W, then a segment, then X, then a segment, then 0, then 5 segments to 5. Wait, maybe each small segment is 1 unit? Wait, no, let's see: from -5 to 0 is 5 units, and there are 5 small segments? Wait, the distance between -5 and 0 is 5, so each small segment is 1 unit. So W is at -4? Wait, no, -5 to W: 1 segment, so W is at -4? Wait, no, -5, then W, then a segment, then X, then a segment, then 0. Wait, maybe the coordinates: Let's assume each tick mark is 1 unit. So -5, then W is at -4? No, wait, the first tick after -5 is W, then next is X, then next is -2, -1, 0, then 1,2,3,4,5 (Y). Wait, maybe the distance between W and X: let's see, from W to X: how many units? Let's count the segments. From W to X: 1 segment? Wait, no, the number line: -5, W, (1 segment), X, (1 segment), -3, (1), -2, (1), -1, (1), 0, (1),1,(1),2,(1),3,(1),4,(1),5 (Y). Wait, maybe each small segment is 1 unit. So W is at -4, X is at -2? Wait, no, that can't be. Wait, maybe the distance from -5 to 0 is 5 units, with 5 intervals, so each interval is 1 unit. So W is at -4 (1 unit from -5), X is at -2 (1 unit from W? No, wait, between -5 and 0, there are two points: W and X. So from -5 to W: 1 unit, W to X: 1 unit, X to 0: 3 units? No, that doesn't make sense. Wait, maybe the number line is marked with each small segment as 1 unit. So -5, -4 (W), -3, -2 (X), -1, 0, 1, 2, 3, 4, 5 (Y). Ah, that makes sense. So W is at -4, X is at -2. Then the length of \(\overline{WX}\) is the absolute difference between their coordinates.

Step2: Calculate the length

The length of a segment between two points \(a\) and \(b\) on a number line is \(|b - a|\). So for W at -4 and X at -2: \(|-2 - (-4)| = |-2 + 4| = |2| = 2\).

Step1: Determine positions of W and Y

From the number line, W is at -4 (as above) and Y is at 5.

Step2: Calculate the length

Using the distance formula on the number line: \(|5 - (-4)| = |5 + 4| = |9| = 9\)? Wait, no, wait, maybe my initial assumption about W's position is wrong. Wait, let's re-examine the number line. The number line has -5, then W, then a mark, then X, then a mark, then 0, then 5 marks to 5. Wait, from -5 to 0: how many segments? Let's count the ticks: -5, W, (tick), X, (tick), 0, (tick), (tick), (tick), (tick), (tick), 5. Wait, from -5 to 0: 5 segments (since -5 to 0 is 5 units, so each segment is 1 unit). So -5, then W is at -4 (1 segment from -5), then tick at -3, X at -2 (2 segments from -5), then tick at -1, 0, then ticks at 1,2,3,4,5 (Y). So W is at -4, Y is at 5. Then the distance is \(5 - (-4) = 9\)? Wait, but let's check again. Wait, maybe the number of segments from W to Y: from -4 to 5, how many units? 5 - (-4) = 9. But let's count the segments. From W (-4) to 0: 4 segments (since -4 to 0 is 4 units), then from 0 to Y (5): 5 segments. Total 4 + 5 = 9. Yes.

Step2: Calculate the length

Length of \(\overline{WY}\) is \(|5 - (-4)| = 9\).

Answer:

2

Problem 6: Length of \(\overline{WY}\)