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Find the point B if M is the midpoint of the line segment joining points A and B.

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3 Answers

Here is a quick way:
You go from A to M in x-direction in 7 units. You go another 7 units to reach B. So, the x-coordinate of B is 6+7 = 13. In the same way, the y-coordinate of B is -1+7 = 6.
 
Answer: B(13, 6)
First, you will need to know the midpoint formula:
M=((x1+x2)/2 , (y1+y2)/2)
 
Let us call A = (x1, y1). This means that x1=-1 and y1=-8.
We know that the midpoint, M, is (6, -1).
B will be the unknown point, (x2, y2).
 
Therefore, we must plug in what we know:
 
(6, -1) = ((-1+x2)/2 , (-8+y2)/2).
 
From here, we will create two equations. One will help us to solve for x2, and the other will help us to solve for y2. We will create the two equations by setting the x value on the left hand side equal to the x value on the right hand side:
 
6 = (-1+x2)/2       {multiplying both sides by 2 gives us}
12 = -1 + x2         {adding 1 to both sides gives us the value for x2}
x2 = 13
 
Now we will need to find y2 using the same method (setting the value for y on the left hand side equal to the value for y on the right hand side).
 
-1 = (-8+y2)/2     {multiplying both sides by 2 gives us}
-2 = -8 + y2        {adding 8 to both sides gives us the value for y2}
y2 = 6
 
Therefore, we know that point B is (13, 6). That is the answer.
 
To check your answer, plug A and B back into the midpoint formula:
M = ((-1 + 13)/2 , (-8 + 6)/2)
M = ((12/2) , (-2/2))
M = (6,-1)
which is correct!

Comments

Instead of memorizing the formula, just think of a midpoint as the average of the x values and the average of the y values.
 
You find the average of two numbers by adding them and dividing by 2.