Question

The number line shown contains three points R, S, and T, whose coordinates have absolute values r, s and t respectively. What is the average (arithmetic mean) of the coordinates of the points R, S and T?

Answer 1

Hint: This is a question of the number line. To solve the above question first we will derive the actual value of coordinates of the given points. Then using arithmetic mean formula or average formula we will derive the answer.

Complete step-by-step answer:
According to the question there are three points given in the number line.
The coordinate of point R is r.
The coordinate of point S is s.
And the coordinate of T is t.
 $ \therefore $ The average value (arithmetic mean) of the coordinates of the point R, S and T = Sum of the coordinates of the points / number of the points given
Here the number of the points given is 3.
 $ \therefore $ The average value (arithmetic mean) of the coordinates of the point R, S and T $ = \dfrac{{r + s + t}}{3} $
But in the given figure, we can see that the point R is in the left side of the point zero in the number line i.e. (midpoint of number line)
That means the actual value of the point R is negative.
Hence the coordinate of point R is –r.
As point S and T are on the right side of the zero in number line, their coordinates are positive.
That means coordinates of points S and T will remain the same.
 $ \therefore $ The average value (arithmetic mean) of the coordinates of the point R, S and T $ = \dfrac{{( - r) + s + t}}{3} $
 $ = \dfrac{{s + t - r}}{3} $

Note: A number line is defined as a straight line with numbers placed at equal intervals along its length. It can be extended to infinity in both directions.
The numbers on the number line increase from left to right and decrease from right to left.
It represents both positive and negative integers. Its midpoint is zero. Integers are positive to the right of zero and negative to the left of the zero.
We can also solve the above question using examples by taking coordinates of the points in numbers.
The average or the arithmetic mean of numerical values is calculated by adding them together and then dividing by the number of terms.
Arithmetic mean or average = $\dfrac{\text{Sum of the given values}}{\text{number of the given values.}}$