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

1 Answer
Johnson Z.
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)|)))#

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