The midpoint M of AB has coordinates (4,9).  If the coordinates of A are (2,8), what are the coordinates of B?

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caledon's profile pic

caledon | High School Teacher | (Level 3) Senior Educator

Posted on

Since M is the midpoint of a linear segment, then by definition the segment from A to M will have the same slope as the segment from M to B.

If we find the slope of AM, and apply it to M, it will lead us to B.

Comparing M and A, we find that there is a +2 change in X, and a +1 change in Y. All we need to do is apply these changes to the coordinates of M;

4(+2), 9(+1)

B = 6,10

dweeks50's profile pic

dweeks50 | eNotes Newbie

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The midpoint between two points (a,b)  and (c,d)  is given by `((a+c)/2, (b+d)/2)`

We have that one point is (2,8). So we can let a=2 and b=8.

We also know the midpoint is (4,9).  

From this information we get the following (4,9) =`((2+c)/2,(8+d)/2)`

Since two points are equal only if both coordinates are equal we have:

To solve the second equation, multiply both sides by 2. This gives you 8 = 2+c. Subtract 2 from both sides to find 6 = c.

To solve the first equation, multiply both sides by 2. This gives you 18=8+d. Subtract 8 from both sides to find d = 10.

So the other point is B = (6,10)

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yamnawaseem's profile pic

yamnawaseem | Student, Grade 11 | (Level 1) eNoter

Posted on

the midpoint has co-ordinates (4,9)

and the co-ordinates of A are (2,8)

need to find co-ordinates of B

(x co-ordinate of A +x coordinate of B)/2= x coordinate of midpoint

so 

(2+x)/2=4

multiply both sides by 2 and you get

(2+x)=8

x=6, you do the exact same thing with the y coordinates 

(8+y)/2=9

(8+y)=18

y=10 so the coordinates of B are (6,10)

rachellopez's profile pic

rachellopez | Student, Grade 12 | (Level 1) Valedictorian

Posted on

I learned a cool trick in school for problems like this. When you are given one point on a line and then the midpoint of the line, you can set up the problem like this:

Point A: (2,8)      Midpoint: (4,9)     Point B: (x,y)

If you count the difference between the x-value of Point A (2) and the x-value of the midpoint (4), you get a difference of 2. If you add 2 to the x-value of the midpoint, you get 6. This is the x-value of Point B. 

You can do the same for the y-value. The difference between the y-value of Point A (8) and the y-value of the midpoint (9) is 1. Adding 1 to the y-value of the midpoint gives you 10 for the y-value of Point B.

This makes Point B=(6,10). That's a cool little shortcut, which I find much easier than remembering an equation. 

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