Question Video: Understanding that the Distance Between Two Points is the Absolute Value of Their Difference Mathematics

Matthew and Daniel were comparing their elevations. Matthew’s position was 15.5 m below sea level, while Daniel’s position was 30 m above sea level. Which of the following expressions represents the difference in elevation between Matthew and Daniel? [A] −15.5 + 30 [B] 15.5 − 30 [C] 30 − 15.5 [D] |30 − 15.5| [E] |30 − (−15.5)| Calculate the difference in elevation.

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Video Transcript

Matthew and Daniel were comparing their elevations. Matthew’s position was 15.5 metres below sea level, while Daniel’s position was 30 metres above sea level. Which of the following expressions represents the difference in elevation between Matthew and Daniel? A) Negative 15.5 plus 30, B) 15.5 minus 30, C) 30 minus 15.5, D) the absolute value of 30 minus 15.5, or E) the absolute value of 30 minus negative 15.5. And the second part, calculate the difference in elevation.

First, we’ll need to figure out the expression for the difference in elevation and then we’ll calculate. We could visualise the difference in elevation. If this base is the sea level, we know that Matthew is 15.5 metres below sea level and Daniel is 30 metres above sea level. The difference between the elevations of Matthew and Daniel will be this space. But how do we write that as an expression?

We know that when we use the word difference, it means subtraction. If we were going to take Daniel’s elevation and subtract Matthew’s elevation, we know that Daniel’s elevation is 30 metres above sea level. But because Matthew is located below sea level, we need to list his elevation with a negative value. We need to say that he is located at negative 15.5 metres of elevation.

We know that when we’re dealing with distances, we need a positive result, which means we want the absolute value of this difference. One expression to find the difference in elevation between Matthew and Daniel would be the absolute value of 30 minus negative 15.5, which is option E.

We now want to try and solve this expression. The absolute value of 30 minus negative 15.5. That’s going to be equal to the absolute value of 30 plus 15.5 because to subtract a negative is to add. 30 plus 15.5 is 45.5. And the absolute value of 45.5 is 45.5.

We can use our diagram to check and see if this makes sense. To get from Daniel to Matthew, you would travel from Daniel’s elevation to sea level, which is 30 metres. And then, you would travel from sea level to Matthew’s elevation, which is 15.5 metres for a total change in elevation of 30 metres plus 15.5 metres, which is 45.5.

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