Question

The midpoint of KL is M(8, 3). One endpoint is L(8, 0). Find the coordinates of the other

endpoint K.

Answer 1

Answer: K(8,6)

Explanation:

M(8,3) - the midpoint of KL L(8,0) K(x,y)=?

`\displaystyle\\Mx=(Kx+Lx)/(2)`

Multiply both parts of the equation by 2:

`2Mx=Kx+Lx\\2Mx-Lx=Kx+Lx-Lx\\2Mx-Lx=Kx\\Mx=8\ \ \ \ Lx=8\\Hence,\\2(8)-8=Kx\\16-8=Kx\\8=Kx\\\\2My-Ly=Ky\\My=3\ \ \ \ Ly=0\\Hence,\\2*(3)-0=Ky\\6-0=Ky\\6=Ky\\Thus,\\K(8,6)`