A is (a,3) and B is (4,b). If the midpoint of AB is (3,5) , what are the values of A and B?

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Answer 1 · 2018-01-05T10:32:59

The points are #A=(2,3)# and #B=(4,7)#.
Also, #a=2# and #b=7#.

Given #(x_1,y_1)# and #(x_2,y_2)#, the midpoint is given by:

#((x_1+x_2)/2,(y_1+y_2)/2 )#.

For points #(a,3)# and #(4,b)# with midpoint #(3,5)# we have:

#((a+4)/2,(3+b)/2 ) = (3,5)#.

This gives us two equations, one for the #x#-coordinate and one for the #y#-coordinate.

For #x#:

#(a+4)/2=3#

multiply by 2:

#a+4=6#

subtract 4:

#a=2#

For #y#:

#(3+b)/2=5#

multiply by 2:

#3+b=10#

subtract 3:

#b=7#

So we have #a=2# and #b=7#.

That means the points are #A=(2,3)# and #B=(4,7)#.