Question

Is there a relationship between the distance and the sum? Is there a relationship between the distance and the difference? A 5-column table with 3 rows. Column 1 is labeled a with entries 1, 4, negative 6. Column 2 is labeled b with entries 2, negative 1, negative 3. Column 3 is labeled a + b with entries 3, 3, negative 9. Column 4 is labeled a minus b with entries negative 1, 5, negative 3. Column 5 is labeled Distance with entries 1 unit, 5 units, 3 units. Which describes the relationship between the distance and the difference? The distance is always the opposite of the difference. The distance is exactly the difference. The distance is the absolute value of the difference. The distance is not related to difference.

Answer 1

The distance is the absolute value of the difference.

Explanation:

Given table:

`\begin{array}c\cline{1-5} a & b & a+b & a-b & \sf distance\\\cline{1-5} 1 & 2 & 3 & -1 & 1 \sf \: unit\\\cline{1-5} 4 & -1 & 3 & 5 & 5 \sf \: units\\\cline{1-5} -6 & -3 & -9 & -3 & 3 \sf \: units\\\cline{1-5}\end{array}`

The difference is column 4.

The distance is column 5.

The absolute value of a number is its positive numerical value. It is denoted by a vertical line either side of the real number.

For example, |5| means 'the absolute value of 5', and |-5| means 'the absolute value of -5'.

Taking the absolute values of the differences:

⇒ |-1| = 1

⇒ |5| = 5

⇒ |-3| = 3

Therefore, the distance is the absolute value of the difference.

Answer 2

• C) The distance is the absolute value of the difference

Explanation:

We are interested in the last two columns.

If we compare them we see that each value of the distance column is the absolute value of corresponding value of difference:

• a - b = 1, 5, - 3
• distance = 1, 5, 3

Corect choice is C