We can use the midpoint formula to find our answer, which is [tex] \Bigg(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\Bigg) [/tex], where [tex] (x_1, y_1) [/tex] and [tex] (x_2, y_2) [/tex] are endpoints of a line.
In this case, we can substitute information we know into the problem to find our answer. We already know one of the coordinates and what the midpoint is, meaning that we can obtain the expression:
[tex] \Bigg(\dfrac{0 + x_2}{2}, \dfrac{4 + y_2}{2}\Bigg) = (-2, 10) [/tex]
We should now solve our problem by setting the first part of the first coordinate with the first part of our midpoint and by setting the second part of the coordinate with the second part of our midpoint, like this:
[tex] \dfrac{0 + x_2}{2} = -2 [/tex] and [tex] \dfrac{4 + y_2}{2} = 10 [/tex]
Now, solve each expression independently:
[tex] \dfrac{0 + x_2}{2} = \dfrac{x_2}{2} = -2 [/tex]
[tex] x_2 = -4 [/tex]
[tex] \dfrac{4 + y_2}{2} = 10 [/tex]
[tex] 4 + y_2 = 20 [/tex]
[tex] y_2 = 16 [/tex]
Our second coordinate, endpoint N, is (-4, 16). The answer is C.
