Question

Point B is the midpoint of the line segment ACIf A = (9, 2) and B = (4, -4), where is C?

Answer 1

You have that A = (9,2), B = (4,-4)

In order to find the coordinates of C, a point at the middle of the segment AC, you calculate the midpoint of each couple of coordinates.

For the first coordinate:

$\frac{9+4}{2}=\frac{13}{2}=6.5$

For the second coordinate:

$\frac{2-4}{2}=\frac{-2}{2}=-1$

Hence, the coordinate of C is C = (6.5 , -1)

For the case of the points (4a,5g) and (-6a,-g), you have:

$\begin{gathered} \frac{4a-6a}{2}=\frac{-2a}{2}=-a \\ \frac{5g-g}{2}=\frac{4g}{2}=2g \end{gathered}$

Hence, the midpoint is (-a,2g)

$\frac{5g-g}{2}=\frac{4g}{2}=2g$