Question

How do you find the missing coordinate if P=(4,-1) is the midpoint of the segment AB, where A=(2, 5)?

Answer 1

`B=(6,-7)`

Explanation:

Recall that the midpoint formula is:

`color(blue)(|bar(ul(color(white)(a/a)M=((x_1+x_2)/2,(y_1+y_2)/2)color(white)(a/a)|)))`

In your case:

Let `M=(4,-1)`
Let `(x_1,y_1)=(2,5)`
Let `(x_2,y_2)=`coordinate of B

Start by plugging your known values into the formula.

`(4,-1)=((2+x_2)/2,(5+y_2)/2)`

Since you are looking for `(x_2,y_2)`, the coordinates of B, you can treat the components of `x` and `y` to be two separate equations. For instance,

`4=(2+x_2)/2color(white)(XXXXXXXX)-1=(5+y_2)/2`

In each equation, solve for the variable.

`8=2+x_2color(white)(XXXXXXXxx)-2=5+y_2`

`x_2=6color(white)(XXXXXXXXXXXx)y_2=-7`

Hence, the coordinate of `B` is:

`B=color(green)(|bar(ul(color(white)(a/a)color(black)(((6,-7)))color(white)(a/a)|)))`