Find the other endpoint using the midpoint and endpoint..

Question

midpoint-(20,21)

endpoint- (17,19)

Answer 1

To go from the first end point to the mid point, you move right 3 and up 2. To find the other end point, you perform the same operation, but starting from the midpoint.

(20+3, 21+2) = (23,23)

Your solution is (23,23)

Answer 2

To solve this problem, it's important to understand what a midpoint and endpoint are on a line. A midpoint is the point at the center of the line, and an endpoint is one of two points on a line where it terminates, or ends. Because the midpoint is at the center, or middle of the line, the distance from the midpoint to either endpoint is exactly equal. Knowing this, we can figure out the other endpoint of the line given in this problem.

Remember, the distance from the endpoint to the midpoint is going to equal to the distance between the points given. So all you really need to do here is find the difference between the x and y coordinates. You can do this by subtract the endpoint's x and y coordinate from the respective midpoint's x and y coordinate, as shown below:

For the x coordinates,

20 - 17 = 3

For the y coordinates,

21 - 19 = 2

So now we take these differences, and add them to the midpoint's respective coordinates, as shown:

For the x coordinate,

20 + 3 = 23

For the y coordinate,

21 + 2 = 23

So the other endpoint is at (23, 23). If you want an easy repeatable equation for this, it could look like the one below:

(x_e2,y_e2 ) = (x_{m +} x_m - x_e1, y_{m +} y_m - y_e1), where x_e2 = endpoint you're looking for's x coordinate

y_e2 = endpoint you're looking for's y coordinate

x_m = midpoint x coordinate

y_m = midpoint y coordinate

x_e1 = given endpoint's x coordinate

y_e1 = given endpoint's y coordinate