Q25 - Geometry

Question

For the following coordinates of two points on a number line, state the distance between the points 2 and $-6$.

Step-by-Step Solution

Answer

The distance between the two points is 8.

Step 1. Apply the absolute difference formula.

The Distance can be calculated by taking the absolute value of the difference of coordinates of points. The absolute difference of two real numbers x and y can be calculated by $\left|x-y\right|$. It describes the distance on the real line between the points corresponding to x and y.

Step 2. Calculate the absolute difference.

Let $x=2$ and $y=-6$ be the coordinates of two points $\left(2, -6\right)$.

Step 3. Step description.

Substitute 2 for x and $-6$ for y to determine the absolute value difference.

$$\begin{gathered} \text{distance}=|x-y| \\ =|2-\left(-6\right)| \\ =|2+6| \\ =8 \end{gathered}$$

Hence, the distance between the two points is 8.