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what are the midpoint coordinates for (6,7) and (4,3)

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2 Answers

Hi, Olivia:
 
1) Consider two points on the number line. As an example, let's take points x=0 and x=2. It is obvious, that the midpoint coordinate is x=1;
2) What if we have x=4 and x=9, for example? Again, the midpoint is x=6.5, since its distance from both points is the same. Indeed, |4-6.5|=|-2.5|=2.5 and |9-6.5|=|2.5|=2.5. Remember, distance is the absolute value of the difference between x-coordinates of the first and the second point.
3) Can we find a formula to obtain the x-coordinate of the midpoint? Let us try.
 
Let the first point be x1 and the second be x2. Let the midpoint be xm. Without losing any generality, let us assume x1<x2. Then x1<xm<x2, since midpoint shall be between two points. We know that distance from midpoint to each of two points is the same. This means that:
xm-x1=x2-xm; Solve for xm,
 
2xm=x2+x1
 
xm=(x1+x2)/2;
 
So the coordinate of a midpoint is just the average of two coordinates.
 
Now, we can generalize. If we consider two points on the plane, with coordinates (x1,y1) and (x2,y2), it is natural to suggest that the coordinates of a midpoint will be given by the average of respective y- and x-coordinates of endpoints. So, we suggest that:
 
(xm,ym)=(½(x1+x2);½(y1+y2)); 
 
And this is indeed the case. So in your example,
 
xm=½(6+4)=5;
ym=½(7+3)=5;
 
or
 
(xm,ym)=(5,5)
 
As a matter of fact, this can be generalized for 3-dimensional case and for any number of dimensions.
mid point formula GO!
(x2+x1)/2  gives the x coordinate
 
(y1+y2)/2 gives the y coordinate
 
(6,7) and (4,3)
 
lets make (6,7) point 1 
xis 6
y1 is 7
 
 
lets make (4,3) point 2
 
x2 is 4
y2 is 3
 
when I was younger labeling the points like that helped me plug everything in correctly
 
so we have 
(4+6)/2  = 10/2 or 5
(7+3)/2 =10/2 or 5
 
so your midpoint is (5,5)

Comments

also if you are finding the midpoint and forget the formula, you can just take the average of the x's and the average of the two y values and you will get the correct midpoint.
if you are given the midpoint and one of the end points, and the question wants you to get the other endpoint, then you must use that formula