Point A is (5, 7). Point B is (x, y). The midpoint of AB is (17, –4). What is the value of B?

We need to use our generalized midpoint formula:

MP = ( (5 + x)/2, (7 + y)/2 )

Solve each separately:

(5 + x)/2 = 17 → 5 + x = 34 → x = 29

(7 + y)/2 = –4 → 7 + y = –8 → y = –15

Therefore, B is (29, –15).

A line's midpoint is the coordinate pair of that line which has the same number of points on either side of it. It bisects the line in two equal parts. 

Solution:

We are given that the line has an endpoint at  and its midpoint is on the origin. This known point would be in the Quadrant III and since on the opposite side of the midpoint there is exactly as much line we know that the other half of our line will lie in the Quadrant I. Add the absolute value of our known point to the coordinates of the origin to get . This is the unknown endpoint. You should recognize that this end point is exactly the same distance in the x and y direction (just opposite) as our given endpoint.

For this kind of problem, it's important to keep in mind how midpoint is solved for:

 where  is the midpoint coordinate.

Because we've been given the midpoint already, we'll have to solve this problem backwards. Since we've been given one of the endpoints (X) and we just need to solve for the other end point (Y), we may arbitrarily assign  as . If we substitute in the two coordinates - an endpoint and the midpoint - we should be able to solve for the unknown endpoint. 

It may be visually easier to break the arithmetic into separate operations. 

 and 

By separating the x and y components, we can easily solve for the missing endpoint now.

Doing similar arithmetic,  will be solved to be .

Therefore, endpoint Y is 

For this kind of problem, it's important to keep in mind how midpoint is solved for:

 where  is the midpoint coordinate.

Because we've been given the midpoint already, we'll have to solve this problem backwards. Since we've been given one of the endpoints (F) and we just need to solve for the other end point (E), we may arbitrarily assign  as . If we substitute in the two coordinates - an endpoint and the midpoint - we should be able to solve for the unknown endpoint. 

It may be visually easier to break the arithmetic into separate operations. 

 and 

By separating the x and y components, we can easily solve for the missing endpoint now.

Doing similar arithmetic,  will be solved to be .

Therefore, endpoint E is .

For this kind of problem, it's important to keep in mind how midpoint is solved for:

 where  is the midpoint coordinate.

Because we've been given the midpoint already, we'll have to solve this problem backwards. Since we've been given one of the endpoints (D) and we just need to solve for the other end point (F), we may arbitrarily assign  as . If we substitute in the two coordinates - an endpoint and the midpoint - we should be able to solve for the unknown endpoint. 

It may be visually easier to break the arithmetic into separate operations. 

 and 

By separating the x and y components, we can easily solve for the missing endpoint now.

Doing similar arithmetic,  will be solved to be .

Therefore, endpoint Y is .

We know that the midpoint of our line segment is  . To find the x-coordinate of this segment, we work backwards, starting with our midpoint formula. In this case, we only need to use the midpoint formula to solve for the x-coordinate, which looks like:

Next, multiply both sides of the equation by 2, which gives us:

, which means our missing x-coordinate is 0. So, the endpoints of our line segment are .

To solve, we will using the midpoint formula and substitute what we know.  The midpoint formula is:

where  and  are the endpoints.

Now, here is what we know:

Here is what we are solving for

So, we will substitute.  We get

We can divide this into parts.  We know

and 

So, we can solve for  and  to find the other endpoint.

This give us the point .  Therefore, the other endpoint is .