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

1 Answer
Jun 15, 2016

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)|)))