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

`=((x_(1)+y_(1))/(2),(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

`=(a+b)/(2)`

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

`=(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.