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: Find Brook's distance

To find the distance between two points on a number - line, we use the formula \(d=\vert x_2 - x_1\vert\). Let's assume the coordinates of the points. If we consider two points, say \(L=-6\) and \(M = - 2\). Then \(d=\vert-2-(-6)\vert=\vert-2 + 6\vert=\vert4\vert = 4\).

Step2: Find Vivian's distance

If we consider the points \(L=-6\) and \(N = 4\). Then \(d=\vert4-(-6)\vert=\vert4 + 6\vert=\vert10\vert
eq6\). If we consider \(M=-2\) and \(N = 4\), then \(d=\vert4-(-2)\vert=\vert4 + 2\vert=6\)

Answer:

Brook measured the distance between \(L\) and \(M\). Vivian measured the distance between \(M\) and \(N\).