Question

A classmate tells you, “Finding the coordinates of a midpoint is easy. You just find the averages.” Is there any truth to it? Explain what you think your classmate means

Answer 1

Yes...there is truth to what ur classmate is saying.

first of all, to find the average of something, u add up all the numbers in ur data, and divide by how many numbers there are.

the midpoint formula : ((x1 + x2)/2 , (y1 + y2)/2)

so lets say ur points are (2,4) and (4,6)

so ur going to add ur x terms (2 + 4)....then divide by 2 (because there are 2 numbers)...so ur basically taking the average of ur two x terms.
you do the same with the y terms.

midpoint is : ((2 + 4)/2 , (4 + 6)/2) = (6/2 , 10,2) = (3,5)

Answer 2

Answer with explanation:

Suppose the coordinates of two points are

            $(x_{1},y_{1}), \text{and},(x_{2},y_{2})$

It's Mid point is given by

        $=(\frac{x_{1}+y_{1}}{2},\frac{x_{2}+y_{2}}{2})$

⇒Mid point formula is used for two points either in one dimensional plane, two dimensional plane or in three dimensional plane.

Since , Average is calculated not only for two observations,it can be calculated for 'n' number of Observations.

→Average of two data values a and b can be calculated by

   $=\frac{a+b}{2}$

→Similarly, mid point of two points having coordinates a and b is equal to

      $=\frac{a+b}{2}$

⇒ Calculating Mid point and Average between two points is same while Calculating Mid point between two points and average for more than two points is not same.