Question

brook states that the distance on the line is 4 units. caleb states that the whole line does not have a distance because it continues on forever. vivian states that the line is 6 units long. which distance did brook measure? which distance did vivian measure?

Explanation:

Step1: Recall distance - formula on number - line

The distance between two points \(a\) and \(b\) on a number - line is \(|a - b|\).

Step2: Find the distance Brook measured

Let's assume Brook measured the distance between two points. If we consider two points such that the distance is 4 units. Let the points be \(x_1\) and \(x_2\) with \(|x_1 - x_2|=4\). Looking at the number - line, if we consider the points \(L=-6\) and \(M = - 2\), then \(|-6-(-2)|=|-6 + 2|=|-4| = 4\). So Brook measured the distance between \(L\) and \(M\).

Step3: Find the distance Vivian measured

If we consider two points such that the distance is 6 units. Let the points be \(y_1\) and \(y_2\) with \(|y_1 - y_2|=6\). Looking at the number - line, if we consider the points \(M=-2\) and \(N = 4\), then \(|-2 - 4|=|-6|=6\). So Vivian measured the distance between \(M\) and \(N\).

Answer:

Which distance did Brook measure? \(L\) to \(M\)
Which distance did Vivian measure? \(M\) to \(N\)