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:

`(9+4)/(2)=(13)/(2)=6.5`

For the second coordinate:

`(2-4)/(2)=(-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} (4a-6a)/(2)=(-2a)/(2)=-a \\ (5g-g)/(2)=(4g)/(2)=2g \end{gathered}`

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

`(5g-g)/(2)=(4g)/(2)=2g`