The midpoint of a line segment is (-1,-3). One endpoint is (7,3). What is the other endpoint?

Question

geomentry 

Answer 1

Using the midpoint formula, if the endpoints are (x1,y1) and (x2,y2) and the midpoint is (x,y), then x = (x1 + x2)/2 and y = (y1 + y2)/2. Since we are trying to find the coordinates of the second endpoint, (x2,y2), let's solve the first equation for x2 and the second equation for y2. This gives us x2 = 2x - x1 and y2 = 2y - y1. Since x = -1 and x1 = 7, we get x2 = 2*(-1) - 7 = -9. And since y = -3 and y1 = 3, we get y2 = 2*(-3) - 3 = -9. Therefore, the other endpoint is (x2,y2) = (-9,-9).

Answer 2

Assume (x1,y1) and (x2,y2) are endpoints, and (m1,m2) is the midpoint.

 

The midpoint formula is [(x1 + x2)/2, (y1 + y2)/2] = (m1, m2)

 

Substitute what you know, [(7 + x2)/2, (3 + y2)/2] = (-1,-3)

 

Then, (7+x2)/2 = -1

and, (3+y2)/2 = -3

 

(7+x2)/2 = -1

*2              *2

 

7+x2 = -2

-7        -7

 

x2 = -9

 

(3+y2)/2 = -3

*2             *2

 

3+y2 = -6

-3         -3

 

y2 = -9

 

(-9,-9)