Which expressions represent the distance between the two points?
Choose all answers that are correct.
The number line shows two points with coordinates negative 11 and positive 7.
|–11 – 7|
|–11 + 7|
|7 – (–11)|
–11 – 7
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If we want to know the distance between two points (i.e. two values) on the number line, then we usually work out:
\[Largest~Value - Smallest~Value\]
In this case, our largest value would be 7 and our smallest -11, as 7 > -11 (it's further to the right on the number line). This should always give us a positive value for our distance, which is what we generally use to represent the 'space' between any two numbers/two points.
Another way we can look at this is if we were to take one number away from the other without wondering which was largest and which was smallest. So, for example, if we wanted to find the 'distance' between the points 3 and 7 on the number line, we could work out:
\[3 - 7 = -4~ or~ 7 - 3 = 4\]
In this case, if we took the absolute value of both of these:
\[|3 - 7| = |-4| = 4\]
\[|7 - 3| = | 4 | = 4\]
our positive distance answer stays as it is and the negative form converts to the positive. Now, it doesn't matter which number we take away from the other, if we take the absolute (or positive) value of our answer, we will get the correct distance between the two. So, to find the distance between two values 'a' and 'b' on the number line, we work out:
\[|a - b|~or~|b - a|, ~ as~both~are~equal\]
So, there should be two answers from the four options (as far as I can see!) which are correct @kosonge .....which ones do you think they are?
Have you any idea on what it might be @kosonge .....remember we can work out |a - b| or |b - a| and get the correct answer. Here, our a and b are 7 and -11!
b and c
C is correct @kosonge .....we're working our |largest - smallest| = |7 - (-11)| = |7 + 11| = |18| = 18. Take another look at B though, remember it should also give us out 18 if it's correct!
If we look at B:
|-11 + 7| = |-4| = 4, which is not the same as the distance we worked out in C. In this case we're working out |smallest + largest|, which is not one of our two options for calculating distance. We've already found |largest - smallest|, which of the remaining 4 options is |smallest - largest|?