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

Answer:

$(-1,8)$

Step-by-step explanation:

1) Completing the question:

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

2) Since the Midpoint equation is:

$Midpoint=\left ( \frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} \right )$

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

$(1,4)=\left ( \frac{3+x_{2}}{2},\frac{0+y_{2}}{2} \right )\\\frac{3+x_{2}}{2}=1 \:\: Cross\:Multiplying\\x_{2}=2-3\\x_{2}=-1\\\frac{0+y_{2}}{2} =4\:\:Cross\:Multiplying\\y_{2}=8\\\left (x_{2} ,y_{2} \right )=\left ( -1,8 \right )$

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

$(1,4)=\left ( \frac{3-1}{2},\frac{0+8}{2} \right )\Rightarrow (1,4)=(1,4)$