Question

M is the midpoint of LN. L has coordinates (1,12) and M has coordinates (-10,-4). Find the coordinates of N.

Answer 1

N(-21,-20)

Explanation:

We can apply midpoint formula to solve for endpoint (N):

`\displaystyle{\text{Midpoint}= \left((x_1+x_2)/(2), (y_1+y_2)/(2)\right)}`

Let
`\displaystyle{x_1 = 1}`,
`\displaystyle{y_1 = 12}` and Midpoint = (-10,-4). Therefore:

`\displaystyle{\left(-10,-4\right)= \left((1+x_2)/(2), (12+y_2)/(2)\right)}`

Solve x with -10 and y with -4:

`\displaystyle{\text{N}\left(x_2,y_2\right) = \left((1+x_2)/(2)=-10, (12+y_2)/(2)=-4\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(1+x_2=-20, 12+y_2=-8\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(x_2=-20-1, y_2=-8-12\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(x_2=-21, y_2=-20\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right)=\left(-21,-20\right)}`

Therefore, the coordinate of N is (-21,-20)