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? the distance between l and m the distance between l and n the distance between m and n

Explanation:

Step1: Find coordinates of points

• Coordinate of \(L=-6\), coordinate of \(M = - 2\), coordinate of \(N=4\)

Step2: Calculate distance between \(L\) and \(M\)

Use the formula \(d=\vert x_2 - x_1\vert\). Here \(x_1=-6,x_2 = - 2\), then \(d=\vert-2-(-6)\vert=\vert-2 + 6\vert=\vert4\vert = 4\)

Step3: Calculate distance between \(M\) and \(N\)

Use the formula \(d=\vert x_2 - x_1\vert\). Here \(x_1=-2,x_2 = 4\), then \(d=\vert4-(-2)\vert=\vert4 + 2\vert=\vert6\vert = 6\)

Answer:

• Brook: the distance between \(L\) and \(M\)
• Vivian: the distance between \(M\) and \(N\)