Question

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.)

Answer 1

`(-1,8)`

Explanation:

1) Completing the question:

Midpoint (1,4) Endpoint (3,0)

2) Since the Midpoint equation is:

`Midpoint=\left ( (x_(1)+x_(2))/(2),(y_(1)+y_(2))/(2) \right )`

Then let's plug the known values into that formula:

`(1,4)=\left ( (3+x_(2))/(2),(0+y_(2))/(2) \right )\\(3+x_(2))/(2)=1 \:\: Cross\:Multiplying\\x_(2)=2-3\\x_(2)=-1\\(0+y_(2))/(2) =4\:\:Cross\:Multiplying\\y_(2)=8\\\left (x_(2) ,y_(2) \right )=\left ( -1,8 \right )`

3) We can check it by plugging the points into the formula.

`(1,4)=\left ( (3-1)/(2),(0+8)/(2) \right )\Rightarrow (1,4)=(1,4)`