Question

If B is the midpoint of AC and A is (4,1) and B is (-3,5), what are the coordinates of C?

Answer 1

Solving for coordinates of the endpoint given the midpoint and the other endpoint

Answer:

$(-10,9)$

Step-by-step explanation:

Recall that if you have the two points, $(x_1,y_1)$ and $(x_2,y_2)$, the midpoint between them is $(\frac{x_1 +x_2}{2}, \frac{y_1 +y_2}{2})$.

We let $x_c$ be the $x$-coordinate of point $C$ and $y_c$ for the $y$-coordinate of point $C$.

The problem tells us that point $B$ is the midpoint of $\overline{AC}$. This means that the point $(-3,5)$ is the same point as $(\frac{4 +x_c}{2}, \frac{1 +y_c}{2})$.

Solving for $x_c$:

$\frac{4 +x_c}{2} = -3 \\ \frac{4 +x_c}{2} \cdot 2 = -3 \cdot 2 \\ 4 +x_c = -6 \\ 4 +x_c -4 = -6 -4 \\ x_c = -10$

Solving for $y_c$:

$\frac{1 +y_c}{2} = 5 \\ \frac{1 +y_c}{2} \cdot 2 = 5 \cdot 2 \\ 1 +y_c = 10 \\ 1 +y_c -1 = 10 -1 \\ y_c = 9$

The coordinates of point $C$ is $(-10,9)$.