I just need to understand how its done. I don't understand the midpoint formula.
What is the midpoint of 12,12 and 2,12?
The midpoint formula is: [(x1 + x2)/2 , (y1 + y2)/2)]
A data point is always given in the form of (x, y). In your question, 12, 12 would be the data point at x = 12 and y = 12 as well as x = 2 and y = 12. These are 2 different points on a graph.
To solve your equation by using the midpoint formula, you must take each x from the data points given to you (12 and 2) and add them together. After adding them together, divide that number by 2. Then, take your y data points of 12 and 12, add them together,
and divide that number by 2. This will give you the midpoint of your 2 data points on a graph.
I hope this was helpful.
You could also think of what the midpoint really is,instead of memorizing formulas. What you are doing is finding the average of the x and y values.
x1 + x2 y1 + y2
( ———— , ———— )
(12, 12) (2 , 12)
↑ ↑ ↑ ↑
(x1 , y1) (x2 , y2)
12 + 2 12 + 12
( ———— , ————— )
(7 , 12) are coordinates of midpoint
The short answer is that the midpoint formula simply calculates the point that is halfway between the start and end points along the x-axis, and the halfway point along the y-axis. Those two midpoints are just the averages of the two x's and the two y's.
xmid = (x1 + x2)/2
ymid = (y1 + y2)/2
The midpoint formula helps you find the point in the middle of two points. Midpoint is short for middle point. Since your points are identified by two coordinates (x,y), you have to find the middle coordinates for x and y. The calculations work like averages, because there are two numbers. So the middle number between two numbers is the average of those two numbers. In your example the middle x-coordinate between 12 and 2 is the average of 12 and 2. (12+2)/2=7 So 7 is the middle x-coordinate between 12 and 2, because 7 is 5 away from 2 and 5 away from 12. The midpoint (middle number) of the y-coordinate is the average of the y-coordinates. (12+12)/2=12 Since there is no other number between 12 and 12, 12 is considered the y-coordinate of the midpoint. Finally, writing the coordinates as an ordered pair (x,y), you have the midpoint (7,12).
Plus if you graph these points and draw a horizontal line segment to connect them, you will see that the midpoint (7,12) is in the middle of the other two points (12,12) and (2,12). Notice that the y-coordinates are the same in your example. When each coordinate has a different value, you can draw right triangles to find the midpoint. Here's a video to how to find the midpoint using the midpoint formula.