If an integer $a$ is pictured on the number line, then the distance from the point on the number line that represents the integer to the origin is $| a |$. Using this idea, explain why $| a - b |$ is the distance between the points that represent the integers $a$ and $b$.
Choose the correct answer below. Select all that apply.
AThe distance between a and b is $| a - b |$ only when $a > b >0$ because the distance between a and b is $a - b =| a - b |$.
BThe distance between a and b is $| a - b |$ only when $a >0$ and $b <0$ because the distance between them is $a +- b = a - b =| a - b |$.
CIf $a > b >0$, then the distance between them is $a - b$ or $| a - b |$. If $a >0$ and $b <0$, then the distance between them is $a +(- b )= a - b =| a - b |$. If $a < b <0$, then the distance between them is $- a -(- b )=- a + b = b - a =| a - b |$.
DThe distance between a and b is $| a - b |$ only when $a < b <0$ because the distance between them is $- a -(- b )=- a + b = b - a =| a - b |$.
Choose the correct answer below. Select all that apply.
AThe distance between a and b is $| a - b |$ only when $a > b >0$ because the distance between a and b is $a - b =| a - b |$.
BThe distance between a and b is $| a - b |$ only when $a >0$ and $b <0$ because the distance between them is $a +- b = a - b =| a - b |$.
CIf $a > b >0$, then the distance between them is $a - b$ or $| a - b |$. If $a >0$ and $b <0$, then the distance between them is $a +(- b )= a - b =| a - b |$. If $a < b <0$, then the distance between them is $- a -(- b )=- a + b = b - a =| a - b |$.
DThe distance between a and b is $| a - b |$ only when $a < b <0$ because the distance between them is $- a -(- b )=- a + b = b - a =| a - b |$.