MHB How do I use the midpoint formula to find the coordinates of point C?

[mathdad]

The coordinates of A and B are A(-1, 2) and B(5, -3). If B is the midpoint of line segment AC, what are the coordinates of C?

I know this question is connected to the midpoint formula. If so, how do I use the formula to find the x and y coordinates of C?

 

[MarkFL]

Let's label the coordinates of point $C$ as $(x,y)$...then (as you correctly surmised), the mid-point formula gives us (since $B$ is said to be the mid-point of $\overline{AC}$):

$$\left(\frac{-1+x}{2},\frac{2+y}{2}\right)=(5,-3)$$

This gives us 2 equations:

$$\frac{-1+x}{2}=5$$

$$\frac{2+y}{2}=-3$$

Solving each will give you the values of $x$ and $y$. :D

 

[mathdad]

Let's label the coordinates of point $C$ as $(x,y)$...then (as you correctly surmised), the mid-point formula gives us (since $B$ is said to be the mid-point of $\overline{AC}$):

$$\left(\frac{-1+x}{2},\frac{2+y}{2}\right)=(5,-3)$$

This gives us 2 equations:

$$\frac{-1+x}{2}=5$$

$$\frac{2+y}{2}=-3$$

Solving each will give you the values of $x$ and $y$. :D

I knew this would lead to two equations. Thank you for your help.