Find the midpoint

Question

M is the midpoint of line segment AB. M is (5, 1) and A is (-1, 6). Find B.

Answer 1

We can also use the midpoint formula to find the other endpoint.

 

 

M = ((x₁ + x₂) / 2   ,   (y₁ + y₂) / 2)

 

where:

M = (5,1)

Point A = (-1,6)

 

We will use Point A as the first point.

 

(5,1) = ((-1 + x₂) / 2  ,  (6 + y₂) / 2)

 

 

Next, establish equations according to x-coordinate and y-coordinate to find Point B.

 

For x-coordinate                                 For y-coordinate

 

5 = (-1 + x₂) / 2                                   1 = (6 + y₂) / 2

 

10 = -1 + x₂                                         2 = 6 + y₂

 

11 = x₂                                                -4 = y₂

 

 

The coordinate of Point B is (11, -4).  Similar to Nathan's solution

 

 

Answer 2

To solve this, we need to find the slope of the line. That means we need to remember rise over run. When we have two point on the line we can use the formula:

(y₂ - y₁) / (x₂ - x₁)

It doesn't matter which point is first as long as the coordinates used remain consistent. Let's make M point 1 and A point 2:

(6 - 1) / (-1 - 5)

5/-6, or -5/6

 

So the slope of this line is -5/6. If we take a look at the points, there is indeed a movement to the right 6 and down 5 between them. Therefore, we need to move over another 6 to the right and down 5:

x-coordinate: 5 + 6 = 11

y-coordinate: 1 - 5 = -4

 

So point B is at (11, -4).